M.Sc Physics Question Paper

Loyola College M.Sc. Physics April 2003 Mathematical Physics Question Paper PDF Download

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034.

M.Sc. DEGREE EXAMINATION – PHYSICS

SECOND SEMESTER – APRIL 2003

PH 2803 / PH 825  –  MATHEMATICAL PHYSICS

 

28.04.2003

1.00 – 4.00                                                                                                      Max : 100 Marks

                                                                PART – A                                       (10´ 2=20 marks)

      Answer ALL questions.

 

  1. Starting from the general equation of a circle in the xy plane A (x2 +y2) + Bx + Cy +D=0 arrive at the z z* representation for a circle.
  2. State Liouville’s theorem.
  3. Develop Laurent series of about z = -2.
  4. Write the Jacobian of the transformation .
  5. Show that the Dirac delta function .
  6. State convolution theorem.
  7. Solve the differential equation + .
  8. Obtain the orthonormalising constant for the series in the interval     (-L, L).
  9. Evaluate using the knowledge of Gamma function.
  10. Generate L2 (x) and L3 (x) using Rodrigue’s formula for laugerre

 

 

 

                                                                PART – B                                      (4´ 7.5=30 marks)

      Answer any FOUR.

 

  1. Obtain Cauchy Rieman equations from first principles of calculus of complex numbers.
  2. Determine a function which maps the indicated region of w plane on to the upper half of the z – plane

v                                                                           y

w plane                                                                    z plane

p                              T

 

Q                      s         u                     p1            Q1                 S1       T1         X

-b                     +b                                                 -1                 +1

  1. Develop half-range Fourier sine series for the function f (x) = x ; 0 < x < 2. Use the results to develop the series .
  2. Verify that the system y11 + ; y1(0) = 0 and y (1) = 0 is a Sturm-Liouville System. Find the eigen values and eigen functions of the system and hence form a orthnormal set of functions.
  3. (a) If f (x) = obtain Parseval’s Identity
    where  Pk (x) stands for Legendre polynomials.
  • Prove that  (x) = 2n – 1 Hn (x) where Hn (x) stands for Hermite polynomials.(4+3.5)

 

 

                                                               PART – C                                      (4´12.5=50 marks)

Answer any FOUR.

 

  1. Show that u (x, y) = Sin x Coshy + 2 Cos x Sinhy + x2 +4 xy – y2 is harmonic Construct f (z) such that u  + iv is analytic.
  2. (a)  Evaluate  using contour integration.

(b)  Using suitable theorems evaluate  c : .                                  (7+5.5)

  1. (a) The current i and the charge q in a series circuit containing an inductance L and
    capacitance C and emf E satisfy the equations L  and i = . Using
    Laplace Transforms solve the equation and express i interms of circuit parameters.
  • Find , where L-1 stands for inverse Laplace transform.                 (3.5)
  1. Solve the boundary value problem . with Y (0, t) = 0; yx (L, t) = 0
    y (x, 0) = f (x) ;  yt (x, 0)  = 0  and  and Interpret physically.
  2. Solve Bessels differential equation using Froebenius power series method.

 

 

 

 

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Loyola College M.Sc. Physics Nov 2003 Statistical Mechanics Question Paper PDF Download

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

M. Sc. DEGREE EXAMINATION – PHYSICS

FIRST SEMESTER – NOVEMBER 2003

PH 1801 / PH 721 – STATISTICAL MECHANICS

06.11.2003                                                                                              Max.   : 100 Marks

1.00 – 4.00

 

PART – A

Answer ALL the questions.                                                                         (10 x 2 = 20)

 

  1. Distinguish between micro states and macro states.

 

  1. What is meant by stationary ensemble?

 

  1. Distinguish between canonical and grand canonical ensembles.

 

  1. How does the vibrational contribution to the specific heat of a system vary with temperature?

 

  1. What is the significance of the temperature To for an ideal Bose-Einstein gas?

 

  1. Sketch the Fermi-Disc distribution function for a gas in 3-d at T = 0 and at T > 0.

 

  1. What are white dwarfs?

 

  1. What is the implication of Einstein’s result for the energy fluctuations of black body radiation?

 

  1. Give the relations which represent the Wiener-Khintchine theorem.

 

  1. Write down the Boltzmann transport equation.

 

 

PART – B

 

Answer any FOUR questions.                                                                                (4 x 7.5 = 30)

 

  1. State and explain the basic postulates of statistical mechanics.

 

  1. Obtain the Sackur-Tetnode equation by considering and ideal gas in canonical ensemble.

 

  1. Apply the Bose-Einstein statistics to photons and obtain Planck’s law for black body radiation. Hence obtain the Stefan-Boltzmann law.

 

  1. Show that the specific heat of an ideal Fermi-Dirac gas is directly proportional to temperature when T << TF.

 

  1. Calculate the energy fluctuation for a canonical ensemble. Show that if the fluctuations are very small, it is practically a micro canonical ensemble.

-2-

 

PART – C

 

Answer any FOUR questions.                                                                              (4 x 12.5 = 50)

 

  1. a) Prove Liouiville theorem.

 

  1. b) Explain Gibbs paradox and discuss how it is resolved. (5 + 7.5)

 

  1. a) Show that Boltzmann counting appears as a natural consequence of the symmetry of wave function in quantum theory.                          (5)

 

  1. b) Discuss the features of Gibbs canonical ensemble. Derive an expression for the probability distribution of the canonical ensemble. (7.5)

 

  1. a) Discuss the thermodynamic properties of an ideal Bose-Einstein gas. (7.5)

 

  1. b) How does Landau explain the super fluidity of He4 using the spectrum of phonons and rotons?              (5)

 

  1. a) Show that the fractional fluctuation in concentration is smaller than the MB case for FD statistics and larger for BE statistics. ( 7.5)

 

  1. b) State and explain Nyquist theorem.              (5)

 

  1. Obtain the Boltzmann transport equation. Using it determine the distribution function in the presence of collisions.

 

 

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Loyola College M.Sc. Physics Nov 2003 Spectroscopy Question Paper PDF Download

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

M. Sc. DEGREE EXAMINATION – PHYSICS

FIRST SEMESTER – NOVEMBER 2003

PH 1804 / PH 725 – SPECTROSCOPY

11.11.2003                                                                                              Max.   : 100 Marks

1.00 – 4.00

PART – A

 

Answer ALL the questions.                                                                         (10 x 2 = 20)

 

  1. How are molecules classified on the basis of moment of inertia? Give one example for each.
  2. The moment of inertia of OCS molecule is 137.95 x 10-47 kg-m2. Calculate the rotation constant.
  3. What type of spectroscopy is best suited for H2? Give reasons.
  4. Explain with an example, the rule of mutual exclusion.
  5. What is Fortrat parabola?
  6. The band origin of a transition in C2 is observed at 19378 cm-1 while the rotational fine structure indicates that the rotational constants in excited and ground states are respectively B1 = 1.7527 cm-1 and B11 = 1.6326 cm-1. Estimate the position of the band head.
  7. Define quadruple moment of a nucleus.
  8. Give the importance of double resonance technique.
  9. Calculate the magnetic field strength required to get transition frequency of 60 MHz for hydrogen nuclei.
  10. A Mossbauer nucleus has spin 1/2 and 3/2 in the ground state and excited state respectively. Sketch the Spectrum when combined electric and magnetic fields are present.
PART – B

 

Answer any FOUR                                                                                     (4 x 7.5 = 30)

 

  1. a) Explain the factors that determine the intensity of a spectral line. Obtain an expression for J at which maximum population occurs.

 

  1. b) The separation between lines in the rotational spectrum of HCl molecules was found to be 20.92 cm-1. Calculate the bond length.

 

  1. a) How many normal modes of vibration area possible for H2O? Show by sketch the fundamental vibrational modes of H2O molecule.

 

  1. b) Outline the theory of Raman spectrum on the basis of (1) Classical theory and (2) Quantum theory.

 

  1. Explain the importance of Franck-Condon principle in explaining the intensity of molecular Spectrum.
  2. Discuss the T1 and T2 relaxation mechanism in NMR. Derive an expression for the relaxation time T1.
  3. Explain with a neat diagram, the functioning of Electron energy loss spectrometer.
-2-
PART – C

 

 

Answer any FOUR                                                                                   (4 x 12.5 = 50)

 

  1. (a) Explain, with theory, the spectrum of a linear diatomic molecule of rigid rotor type. Deduce the correction for non-rigid type.

 

(b) Calculate the frequency of  NO  molecule whose force constant is 1609 Nm-1.

 

  1. (a) Explain Born-Oppenheimer      Describe, with theory,  the rotation – vibration spectra of a diatomic molecule.

 

(b) The fundamental and first overtone transition of   14N, 16O are centered at 1876.06 cm-1 and 3724.20 cm-1 respectively. Equivalent the equilibrium frequency, anharmonicity constant and zero point energy.

 

  1. Obtain an expression for the Dissociation energy of a molecule. The Vibrational Structure of the absorption Spectrum of O2 becomes a continuum at 56,876 cm-1. If the upper electronic state dissociates into one ground state atom and one excited atom with excitation energy 15,875 cm-1, estimate the dissociation energy of ground state of O2 in cm-1 and kJ / mole.

 

  1. Explain the principle of ESR. Sketch a neat diagram and explain the functioning of ESR Spectrometer.

 

  1. Outline the importance of ‘RAIRS’ technique in characterising the absorbed surfaces on a specimen.

 

 

 

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Loyola College M.Sc. Physics Nov 2003 Solid State Physics Question Paper PDF Download

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

M.Sc. DEGREE EXAMINATION – PHYSICS

THIRD SEMESTER – NOVEMBER 2003

PH 3801 / PH 921 – SOLID STATE PHYSICS

 

05-11-2003                                                                                            Max.   : 100 Marks

1.00 – 4.00

 

PART – A

 

Answer ALL question.                                                                                (10 x 2 = 20)

 

  1. Define the reciprocal lattice vector .

 

  1. What is a Van der Waal’s interaction?

 

  1. Outline the principles involved in the inelastic scattering of neutrons by PHONONS.

 

  1. State the implications of observing harmonic lattice vibrations.

 

  1. What is size effect?
  2. State Mathiessen rule
  3. What is a Fermi sphere?

 

  1. Distinguish between metals and insulators on the basis of energy bands and the number of electrons per primitive cell.

 

  1. State the difference in the paramagnetic behaviour of rare earth and iron group salts.

 

  1. State Curie-Weiss law and its significance.

 

PART – B

Answer any FOUR questions only                                                             (4 x 7.5 = 30)

 

  1. Obtain the dispersion relation for the one dimensional monoatomic lattice and PLOT w  .

 

  1. Discuss how the nearly FREE electron model for a monoatomic lattice of lattice constant ‘a’ establishes origin of energy gap.

 

  1. What are the three different zone schemes for studying Fermi surface? Explain.

 

  1. Describe the three phonon collision process and briefly EXPLAIN its role in causing thermal resistivity.

 

  1. What are Magnons? Show that the fractional change of magnetization is proportional to T3/2.

-2-

 

PART – C

 

Answer any FOUR questions only.                                                          (4 x 12.5 = 50)

 

  1. Obtain the wave equation for an electron in a periodic potential of lattice constant ‘a’. Hence give the proof of Bloch theorem.

 

  1. a) Derive a quantitative expression for the electronic heat capacity of a free electron gas at low temperatures.     (8.5)

 

  1. b) Quantitatively account for the electrical conductivity as a motion of the Fermi sphere.      (4)

 

  1. a) Apply quantum theory to obtain Curie’s law of para magnetism. (8)

 

  1. b) Describe briefly de Haas Van Alphen effect.     (4.5)

 

  1. a) Explain Ferromagnetic domains. (5)

 

  1. b) Establish theoretically the existence of Bloch Wall between domains in a ferromagnet.                                                         (7.5)

 

  1. Write short notes on any TWO of the following

 

  1. DEBYE’S T3-law.
  2. Isoentropic cooling by demagnetization
  • Paulis Spin paramagnetism

 

 

 

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Loyola College M.Sc. Physics Nov 2003 Solid State Physics II Question Paper PDF Download

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

M.Sc. DEGREE EXAMINATION – PHYSICS

FOURTH SEMESTER – NOVEMBER 2003

PH 4801 / PH 1017 – SOLID STATE PHYSICS II

 

30.10.2003                                                                                          Max.   : 100 Marks

1.00 – 4.00

 

 

PART – A

 

Answer all the questions.                                                                                 (10 x 2 = 20)

 

  1. Explain the physical basis of the effective mass.

 

  1. Discuss the Mott – metal insulation transition with a suitable example.

 

  1. List the microwave and infrared properties of superconductors.

 

  1. Outline briefly, the various methods of measuring the B.E of excitons.

 

  1. Explain the nature of piezoelectricity and hence obtain the piezoelectric equations for polarization and elastic strain.

 

  1. What is meant by “zero field splitting”?

 

  1. Discuss the role of isotope effect on superconductivity.

 

  1. With necessary diagrams, explain the mechanism responsible for the mobility of a dislocation.

 

  1. Distinguish between the Burger vector of a screw dislocation and that of an edge dislocation.

 

  1. Explain the formation of a hole trapped color centre with suitable example.

 

PART – B

 

Answer any FOUR questions only                                                                   (4 x 7.5 = 30)

 

  1. Explain the thermoelectric effects in semiconductors and hence obtain the Kelvin’s relation for irreversible thermodynamics.

 

  1. Derive the dispersion relation for electromagnetic waves and discuss in detail the conditions to be satisfied for the propagation or attenuation of em waves.

 

  1. State the essential conditions required in the formation of Freckle exciton and obtain the energy eigen values.

 

  1. Explain the thermodynamics of the super conducting transition and obtain the expression for stabilization energy density of the super conducting state at absolute zero.

 

  1. Discuss in detail, the Landau’s theory of phase transition and explain the second order phase transition.

-2-

 

 

PART – C

 

Answer any FOUR questions only.                                                                (4 x 12.5 = 50)

 

  1. Derive the expression for the intrinsic carrier concentration and hence form the law of mass action. Prove that the Fermi level lies in the middle of the forbidden gap.

 

  1. a) Discuss in detail, the electrostatic screening behavior of electron gas and obtain the

relation connecting the es potential and charge concentration.                             (7)

 

  1. Using the Thomas-Fermi approximation, derive the expression for the dielectric function of an electron gas.             (5.5)

 

  1. a) Distinguish between A.C. Josephson and D.C. Josephson effects. (3.5)

 

  1. b) Prove that the current of superconductor pairs across the junction depends on the phase difference  in the case of D.C Josephon effect.                                                       (9)

 

  1. Derive the Block equations of motion and obtain the equations for (i) the power absorption and (ii) half width of the resonance at half maximum power.

 

  1. a) What are lattice vacancies? Explain the mechanisms of forming the Schottky and Freckle defects with relevant diagrams.             (5.5)

 

  1. b) Derive the expression for the number of defects formed in the Schottky type with special references to ionic crystals. (7)

 

 

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Loyola College M.Sc. Physics Nov 2003 Quantum Mechanics II Question Paper PDF Download

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

M. Sc., DEGREE EXAMINATION – PHYSICS

THIRD SEMESTER – NOVEMBER 2003

PH 3800 / PH 920 – QUANTUM MECHANICS II

 

03.11.2003                                                                                           Max.   : 100 Marks

1.00 – 4.00

SECTION – A

 

Answer ALL the questions.                                                                         (10 x 2 = 20)

 

  1. If the eigen values of A are ‘a’, then show that where  is the projection operator.
  2. Prove that e-i a Px / is unitary when a is a real parameter.
  3. Evaluate <jm | J – J + | jm>
  4. Show that e
  5. What is first Born approximation?
  6. State optical theorem.
  7. Explain dipole approximation.
  8. What are allowed and Forbidden transitions with respect to the selection rules of the dipole approximation.
  9. Mention the disadvantage of Klein – Gordan equation for relativistic particles.
  10. What is the significance of the negative energy state?

 

SECTION – B

 

Answer any FOUR questions.                                                                                (4 x 7.5 = 30)

 

  1. Show that has the form – i in the Schroedinger representation.
  2. Obtain the G.  Coefficients  for  the  coupling  of  two  spin  angular  momenta  (j1 = j2 = ½).
  3. Arrive at an expression for the scattering amplitude using Green’s functions.
  4. Explain the Schroedinger picture of time evolution.
  5. Obtain the explicit form for matrices in the Dirac Hamiltonian.

 

SECTION – C

 

Answer any FOUR questions.                                                                              (4 x 12.5 = 50)

 

  1. Arrive at an expression for a proper choice of basis set for commuting operators.
  2. Obtain the  matrix  representation for  J2, Jx,  Jy, Jz  in the |jm> basis for j = 1 and j = 3/2.
  3. Explain the partial wave analysis and derive an expression for the scattering amplitude in terms of phase shifts.
  4. Derive an expression for transition probability of upward and downward transition for an atom interacting with an electromagnetic radiation.
  5. Determine the eigenvalues and eigenfunctions of a free particle using Dirac’s Haneiltonian.

 

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Loyola College M.Sc. Physics Nov 2003 Quantum Mechanics I Question Paper PDF Download

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

M.Sc. DEGREE EXAMINATION – PHYSICS

SECOND SEMESTER – NOVEMBER 2003

PH 2801 / PH 821 – QUANTUM MECHANICS  I

 

29.10.2003                                                                                             Max.   : 100 Marks

1.00 – 4.00

 

SECTION – A

 

Answer ALL the questions.                                                                             (10 x 2 = 20)

 

  1. Calculate the Compton shift in wavelength for an electromagnetic radiation of l = 6000 Å while the scattering angle is 30o.

 

  1. Find the de Broglie wavelength of an electron of energy 10 MeV.

 

  1. Show that i (A+ – A) is a hermitian operator for any A.

 

  1. Show that AB is hermitian only if [A,B] = 0 while A, B are hermitian.

 

  1. Show that if any operator commutes with the parity operator, then the eigen functions of non-degenerate eigen values have definite parity.

 

  1. If the probability densities are P1, P2, P3 and P4 for the do mains –a < x <- a/2; -a/2 < x < 0; 0 < x < a/2 ; a/2 < x <a respectively, what is P1 + P2 + P3 + P4 ?

 

  1. Explain the basic assumptions of the perturbative technique.

 

  1. Explain briefly WKB approximation.

 

  1. Show that [Lx, Ly] = i  L2.
  2. Show that esatisfies the equation .

 

 

SECTION – B

 

Answer any FOUR questions.                                                                         (4 x 7.5 = 30)

 

  1. Explain photo electric effect using the quantum theory of radiation.

 

  1. State and prove Ehrenfest’s theorem.

 

  1. (a) Explain the closure property.

 

(b) Give the physical interpretation of eigen values and eigen functions.

 

  1. Obtain the energy eigen values for the single harmonic oscillator.

 

  1. Explain the removal of degeneracy in a doubly degenerate case using time independent perturbation technique.

-2-

 

SECTION – C

 

Answer any FOUR questions.                                                                      (4 x 12.5 = 50)

 

  1. (a) Explain the variation of heat capacity with temperature for solids. (6)

 

(b) Obtain an expression for the Compton shift.                                                    (6.5)

 

  1. Explain the concept of quantum mechanical tunneling and show that the probability of barrier penetration is non-zero.

 

  1. (a) State and prove Heisenberg’s uncertainly                                         (7.5)

 

(b) If [A, H] = 0, show that A becomes a constant of motion.                              (5)

 

  1. (a) Express L2 in spherical polar coordinates. (3)

 

(b) Solve the eigen value equation for L2.                                                              (9.5)

 

  1. Explain the ground state of Hydrogen molecule by using the variational technique.

 

 

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Loyola College M.Sc. Physics Nov 2003 Mathematical Physics Question Paper PDF Download

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

M. Sc. DEGREE EXAMINATION – PHYSICS

SECOND SEMESTER – NOVEMBER 2003

PH 2803 / PH 825 – MATHEMATICAL PHYSICS

 

15.11.2003                                                                                                  Max.   : 100 Marks

1.00 – 4.00

 

PART – A

 

Answer ALL the questions.                                                                              (10 x 2 = 20)

 

  1. Express x2 + y2 = 25 in zz* and reirepresentation.

 

  1. State Liouville’s theorem.
  2. Find Laurent Series of at z = 1 and name the Singularity.
  3. Find the Jacobian of transformation of w = z2.

 

  1. Find L (FÎ (t)), where FÎ (t) represents Dirac delta function.

 

  1. State parseval’s theorem.

 

  1. Obtain the orthonormalizing constant for the set of functions given by ; n = 1, 2, 3  . . . .   in the interval –L to +L.

 

  1. Solve the differential equation y¢ + k l2 y = 0.

 

  1. Write Laplace equation in spherical polar co-ordinates.

 

  1. Using Rodrigue’s formula for Legendre polynomials, evaluate P3(x).

 

PART – B

 

Answer any FOUR.                                                                                         (4 x 7.5 = 30)

 

  1. Derive the necessary conditions for a function to be analytic.

 

  1. Find the residues of f(z) = at its poles.

 

  1. Expand f(x) = sin x, 0 < x < p in a fourier cosine series and hence prove that

 

 

(P.T.O)

-2-

 

 

 

 

  1. Verify that the system y¢¢ + ly = 0; y¢ (0) = 0 and y(1) = 0 is a Sturm-Liouville system. Find the eigenvalues and eigenfunctions of the system. Prove that eigenfunctions are orthogonal.

 

  1. Prove that Ln+1(x) = (2n + 1 – x)Ln(x) – n2  Ln-1(x) where L’s stand for Laugerre polynomials.

 

PART – C

 

Answer any FOUR.                                                                                       (4 x 12.5 = 50)

 

  1. (i) Evaluate along

 

  1. the parabola x = 2t, y = t2 + 3

 

  1. straight lines from (0, 3) to (2,3) and then from (2,3) to (2,4) and

 

  1. a straight line from (0, 3) to (2, 4).    (7.5)

 

(ii) State and prove Poisson’s Integral formula for a circle.                                       (5)

 

  1. Using contour Integration, evaluate for a>|b|.

 

  1. An Inductor of 2 henrys, a resistor of 16 ohms and a capacitor of 0.02 farads are connected in series with an e.m.f E volts. Find the charge and current at any time t>0 if a) E =  300 V and   b) E = 100 sin 3t Volts

 

  1. Generate Set of orthonormal functions from the sequence 1, x, x2, x3 . . . . using Gram-Schmidt orthonormalization process.

 

  1. Write Bessel’s differential equation and obtain the standard solution.

 

 

 

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Loyola College M.Sc. Physics Nov 2003 Electrodynamics II Question Paper PDF Download

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

M. Sc. DEGREE EXAMINATION – PHYSICS

THIRD SEMESTER – NOVEMBER 2003

PH 3802 / PH 922 – ELECTRODYNAMICS II

07.11.2003                                                                                             Max.   : 100 Marks

1.00 – 4.00

 

PART – A

 

Answer ALL questions.                                                                               (10 x 2 = 20)

 

  1. Write down the real electric and magnetic fields for a plane monochromatic wave of amplitude Eo, frequency w, and phase angle that is travelling in the negative y – direction and polarised in the z – direction

 

  1. What is anomalous dispersion?

 

  1. Why are the ‘retarded potentials’ so called?

 

  1. State the Larmor formula for the power radiated by a moving point charge.

 

  1. Define Contra – and Covariant tensors of rank – 2 by their transformation properties.

 

  1. What is the Darwin Lagrangian? Give an expression for the same.

 

  1. Write down the electrodynamic boundary conditions near the surface of a perfect conductor.

 

  1. Distinguish between TM and TE waves.

 

  1. How are the electric and the magnetic fields, in a perfectly conducting fluid, related?

 

  1. State the principle of the ‘pinch’ effect.

 

PART – B

 

Answer any FOUR questions                                                                     (4 x 7.5 = 30)

 

  1. Derive expressions for the reflection and the transmission Coefficients for normal incidence of a plane em wave at the boundary between two linear media.

 

  1. An in finite straight wire carriers the current

 

 

 

0, for t £ 0

I(t)  =                           .     Find the resulting electric field.

Io, for t > 0

 

-2-

 

  1. a) Prove that  the charge  density  transforms  like  the  time  component  of  the  4 – vector.                                                                                                       (2)

 

  1. b) Obtain an expression for the relativistic Lagrangian for a charged particle.

(5.5)

 

  1. Assuming a sinusoidal time dependence for the em fields inside a cylindrical wave guides establish the Maxwells equations in terms of transverse and parallel components.

 

  1. Use the necessary em equation’s to explain the role played by the ‘magnetic Reynolds number’ to distinguish between the diffusion of magnetic lines of force and the freezing – in of the magnetic lines of force.

 

PART – C

 

Answer any FOUR questions                                                                   (4 x 12.5 = 50)

 

  1. Explain the dispersion phenomenon in nonconductors and hence obtain the Cauchy’s equation.

 

  1. Derive expressions for the electric and magnetic fields of an oscillating electric dipole.

 

  1. Write down the field-strength tensors explicitly in matrix form and establish the covariance of the Maxwell’s equations

 

  1. Discuss the propagation of TE Waves in a rectangular wave guide with inner dimensions a, b (with a = 2b) and find the frequencies of the first four modes.

 

  1. Discuss the magneto hydrodynamic flow between boundaries with crossed electric and magnetic fields and bring out the role played by the Hartmann number.

 

 

 

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Loyola College M.Sc. Physics Nov 2003 Electrodynamics I Question Paper PDF Download

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

M.Sc. DEGREE EXAMINATION – PHYSICS

SECOND SEMESTER – NOVEMBER 2003

PH 2800 / PH 820 – ELECTRODYNAMICS I

 

28.10.2003                                                                                          Max.   : 100 Marks

1.00 – 4.00

 

PART – A

 

Answer ALL the questions.                                                                                                      (10 x 2 = 20)

 

  1. Explain the statement that “electrostatic energy does not obey a superposition principle”.

 

  1. List any four basic properties of conductors in an electrostatic field.

 

  1. What are the two properties of an electrostatic potential which lead to a solution of Laplace’s equation in 3-dimensions?

 

  1. Define the Legendre polynomial by the Rodrigues formula and hence write down the 3rd order polynomial.

 

  1. Write down the expressions for the torque and the force on an electric dipole placed in an external electric field.

 

  1. State the relation between the applied electric field and the polarization vector in an anisotropic crystal.

 

  1. Define the surface current density and the volume current density in terms of the current .

 

  1. What is a linear magnetic material? State the relation between the magnetic permeability and susceptibility.

 

  1. State Faraday’s law of em induction in differential form.

 

  1. Give an expression for the Maxwell stress tensor.

 

PART – B

 

Answer any FOUR questions.                                                                          (4 x 7.5 = 30)

 

  1. Find the energy of (a) a uniformly charged spherical shell and (b) a uniformly charged solid sphere.                                                                          (3.5 + 4)

 

  1. A point charged is situated near an infinitely grounded conducting plane. By the method of electrical images, find the amount of induced charge.

 

  1. Derive an expression for the potential of an electrically polarized object in terms of bound charged.

 

  1. Explain the mechanism responsible for diamagnetism.

 

  1. Derive an expression for the mutual inductance of a pair of coils.

 

-2-

 

PART – C

 

Answer any FOUR questions.                                                                       (4 x 12.5 = 50)

 

  1. a) Find the potential of a uniformly charged spherical shell of radius R for points outside and inside.                                                                                                     (9)

 

  1. b) Check whether =  is a possible electrostatic field

(k = a constant).                                                                                             (3.5)

 

  1. Obtain the multipole expansion of electrostatic potential of an arbitrary localized charge distribution. Also explain the term “dipole moment” of the distribution.

 

  1. Derive the Clausius – Mossotti formula which relates the polarizability to the dielectric constant.

 

  1. a) Explain the domain theory of ferromagnetism.   (5)

 

  1. b) Bring out the Salient features of a hysteresis loop of ferromagnetic substance (7.5)

 

  1. a) Explain the potential formulation of electrodynamics.

 

  1. b) Explain the gauge transformation and bring out the differences between the Coulomb gauge and the Lorentz gauge

 

 

 

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Loyola College M.Sc. Physics Nov 2004 Spectroscopy Question Paper PDF Download

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 34.

  1. Sc., Degree examination – PHYSICS

First semester – NOVEMBER 2004

PH 1804 –  Spectroscopy

 

Date : 25.10.2004                                       Max. 100 Marks

Duration: 9.00 – 12.00                         Hours : 3 Hrs

 

 

PART – A

 

 

Answer all the questions                                              (10 X 2 = 20)

 

  1. Classify the type of molecule according to structure from the following list H2O, CO2, CCl4, NH3
  2. Calculate the rotational constant of the H2 molecule. Given that the H-H bond length is 74. 12 pm.
  3. Sketch the fundamental vibrational modes of H2O molecule
  4. State the rule of mutual exclusion
  5. What is Fortrat parabola? Explain its significance
  6. The absorption spectrum of O2 shows vibrational structure, which becomes continuum at 56.876 cm-1. The upper electronic state dissociates into one ground state atom and one excited atom (spectral position at 15875 cm-1). Estimate the dissociation energy of ground state O2 in KJ/mol.
  7. Calculate the value of nuclear magneton
  8. Sketch the H-NMR spectrum of CH3CH2OH
  9. Calculate the recoil velocity of a free Mossbauer nucleus of mass 1.67 X 10 –25 kg, when it emits gamma ray of wavelength 0.1 nm.
  10. Mention any two limitations of surface spectroscopy

 

 

PART – B

 

Answer any four                                                  (4 X 7.5 = 30)

 

  1. Obtain an expression for J for maximum population. The rotation spectrum of a sample has a series of equidistant lines spaced 0.7143 cm-1 apart. Find which transition gives rise to the most intense spectral line at 27°C

 

  1. Describe with theory the rotation – vibration spectra of a diatomic molecule

 

  1. What is Franck-Condon principle? Using the same, explain the intensity of spectral lines

 

  1. Discuss the effect of electric and magnetic fields on Mossbauer spectrum exhibited by 57 Fe.

 

  1. Outline the principle of Electron Energy Loss Spectroscopy and mention the applications

 

PART –  C

 

 

Answer any four                                                            (4 X 12.5 = 50)

 

16a) Explain, with necessary theory, the rotational spectrum of a diatomic molecule of the rigid-rotor type. Deduce the spectrum of non-rigid rotor type molecule.                                                                                        (10)

  1. b) The bond-length of nitrogen molecule is 0.10976 nm. Calculate the seperation between Raman lines. (2.5)

 

  1. a) Outline the theory of Raman effect on the basis of i) classical theory ii) quantum theory.                                                                    (8)
  2. b) The fundamental band of CO is centered at 2143 cm-1 and the first overtone band at 4259.7 cm-1. Calculate i) fundamental frequency of vibration ii) anharmonicity constant iii) zero point energy (4.5)

 

  1. Discuss in detail, the method of characterizing samples using Electron spectroscopy for chemical analysis

 

  1. Discuss in detail, the shielding and de-shielding phenomenon in nuclear magnetic resonance spectroscopy. Explain how the spectral splitting is explained using family tree method.

 

  1. Explain the principles of Auger electron spectroscopy.

 

 

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Loyola College M.Sc. Physics Nov 2006 Statistical Mechanics Question Paper PDF Download

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             LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034  M.Sc. DEGREE EXAMINATION – PHYSICS

AC 11

FIRST SEMESTER – NOV 2006

         PH 1806 – STATISTICAL MECHANICS

(Also equivalent to PH  1801)

 

 

Date & Time : 26-10-2006/1.00-4.00           Dept. No.                                                       Max. : 100 Marks

 

 

 

PART A ( 20 MARKS )

 

ANSWER ALL QUESTIONS.                                        10 X 2 = 20

 

  1. State the ergodic hypothesis. Is it true?
  2. What is meant by stationary ensemble?
  3. When is the classical limit of the quantum description of systems valid?
  4. State the condition for mechanical equilibrium between two parts of a composite system.
  5. State two features of the Gibb’s canonical ensemble.
  6. What is the significance of the temperature T0 for an ideal Bose gas?
  7. Does the chemical potential of an ideal Fermi gas depend on temperature?
  8. What is the implication of Einstein’s result for the energy fluctuations of black body radiation?
  9. What is a stationary Markoff process?
  10.  Write down the Boltzman transport equation.

 

PART B ( 30 MARKS )

 

ANSWER ANY FOUR QUESTIONS.                     4 X 7.5 =30

 

 

 

  1. State and explain the basic postulates of statistical mechanics.

 

  1. Obtain the distribution for an ideal Fermi gas.

 

 

  1. Apply the Bose- Einstein statistics to photons and obtain the Planck law of black body radiation.

 

  1. Discuss the temperature dependence of the energy, specific heat and entropy of an ideal Bose gas.

 

 

  1. Calculate the concentration fluctuation for a grand canonical ensemble. Show that for an ideal classical gas it increases as the volume of the gas decreases.

 

 

 

 

 

 

 

 

PART C ( 50 MARKS )

 

 

ANSWER ANY FOUR QUESTIONS.                                    4 X 12.5 = 50

 

 

 

  1. (a) Prove Liouville theorem. Use it to arrive at the principle of conservation of density in phase space.

(b) Explain the principle of conservation of extension in phase space.

 

17.Calculate the entropy of an ideal Boltzman gas using the micro canonical ensemble. Explain the corrections to be made to obtain the Sackur-Tetrode equation.

 

18.Calculate the pressure exerted by a Fermi-Dirac gas of relativistic electrons in the ground state. Use the result to explain the existence of the Chandrasekhar limit on the mass of a white dwarf.

 

19.Discuss Brownian motion in 1-d and obtain an expression for the particle concentration as a function of (x,t). Explain how Einstein estimated the particle diffusion constant.

 

  1. Derive the Boltzmann transport equation. Use it to find the distribution function in the absence of collisions.

 

 

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Loyola College M.Sc. Physics Nov 2006 Statistical Mechanics Question Paper PDF Download

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             LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034  M.Sc. DEGREE EXAMINATION – PHYSICS

AC 15

FIRST SEMESTER – NOV 2006

         PH 1810 – STATISTICAL MECHANICS

 

 

Date & Time : 26-10-2006/1.00-4.00           Dept. No.                                                       Max. : 100 Marks

 

 

 

PART A (20 MARKS)

 

 

ANSWER ALL QUESTIONS                                      10 X 2 = 20

 

 

  1. State the ergodic hypothesis.
  2. State the principle of conservation of extension in phase space.
  3. When is the classical limit of the quantum description of a system valid?
  4. Sketch the Maxwell velocity distribution.
  5. Why is the super fluid transition in Helium known as the lambda transition?
  6. What is the significance of the fermi temperature?
  7. What is the pressure exerted by a Fermi gas at absolute zero?
  8. How is the super fluidity of Helium-3 explained?
  9. Give Einstein’s relation for the particle diffusion constant.
  10. Define spectral density for a randomly fluctuating quantity.

 

PART B (30 MARKS)

 

 

ANSWER ANY FOUR QUESTIONS                         4 X 7.5 = 30

 

 

  1. Discuss the quantum picture of a micro canonical ensemble.

 

  1. Obtain the distribution for an ideal Fermi gas.

 

 

  1. Apply the Bose  Einstein statistics to photons and obtain the Planck law for black body radiation.

 

  1. Find the temperature dependence of the chemical potential for an ideal FD gas.

 

 

  1. Discuss the random walk problem in 1-d and apply the results to a system of N particles each having a magnetic moment m.

 

 

 

 

 

 

 

 

PART C (50 MARKS)

 

 

ANSWER ANY FOUR QUESTIONS.                                    4 X 12.5 = 50

 

 

  1. Calculate the entropy of an ideal Boltzmann gas using the micro canonical ensemble. Explain the corrections to be made to obtain the Sackur-Tetrode equation.

 

  1. (a) Discuss the features of the Gibb’s canonical ensemble.

(b) Discuss the rotational partition function for a system of diatomic molecules.

 

  1. Discuss the thermodynamic properties of an ideal Bose-Einstein gas.

 

  1. Calculate the pressure exerted by a FD gas of relativistic electrons in the ground state. Use the result to explain t5he existence of Chandrasekhar limit on the mass of a white dwarf.

 

 

  1. (a) Show that the fractional fluctuation in concentration is smaller than the MB case for FD statistics and larger for BE statistics.

(b) Obtain Einstein’s result for the energy fluctuations of black body radiation. What is the implication of the result?

 

 

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Loyola College M.Sc. Physics Nov 2006 Electronics – I Question Paper PDF Download

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                         LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

M.Sc. DEGREE EXAMINATION – PHYSICS

AC 13

FIRST SEMESTER – NOV 2006

PH 1808 – ELECTRONICS – I

 

 

Date & Time : 31-10-2006/1.00-4.00     Dept. No.                                                       Max. : 100 Marks

 

 

PART – A

  1. Draw the circuit diagram of an Integrator using an operational amplifier.
  2. State any two advantages of a R-2R D/A converter over a binary weighted D/A converter.
  3. Develop an ASM program for µP 8085 which sets the C register to 1 if the MSB or LSB of the number at memory location 8100h is ‘1’ else sets C register to 0.
  4. Develop a subroutine for µP 8085 to find the factorial of the number passed to it through the B register.
  5. Develop a program for µP 8085 to convert a two digit packed BCD number in register A to unpacked BCD format in BC register pair.
  6. Develop a program for µP 8085 to generate a square wave in SOD line.
  7. Develop a program segment for µP 8085 to mask RST5.5 and enable the rest.
  8. Write notes on the ALE and READY lines of µP 8085.
  9. State the advantage of relative branching available in Z80 over absolute branching.
  10. Develop an ASM program for µP Z80 to input 40 bytes from I/O port 30h and to store them from 8100h using string primitives.

 

PART – B

  1. Sketch neat circuit diagrams of Op-amp based inverting and non-­inverting amplifiers. Also derive expressions for their voltage gains. (6+6.5)
  2. With timing diagram, explain the instruction cycle for LXI H,FFFFH of µP 8085.
  3. If the crystal frequency of an 8085 system is 1 M.Hz, calculate the delay generated by the following segment of code.

MVI A,50H

rpt:       DCR A

JNZ rpt

  1. Write notes on the software and hardware interrupts available in µP 8085.
  2. Explain the various block transfer and block search instructions available in µP Z80.

 

PART – C

  1. Develop an interface and program for µP 8085 to implement an 8 bits successive approximation A/D converter.
  2. Develop a program for µP 8085 to solve n1Cr1 – n2Cr2 . Use a subroutine for factorial.
  3. There are eight LEDs and two switches (S0 and S1) connected to ports, PA and PB respectively. Develop an ASM program for mP 8085 to generate the following pattern.
S1 S0 LEDs
0 0 OFF
0 1 Binary Ascending
1 0 Left to Right
1 1 All Blinking

 

  1. Explain memory mapped I/O and I/O mapped I/O schemes of m Also explain with a neat circuit diagram how I/O mapped I/O scheme can be implemented with address decoding for 2 ROM chips of 8KB each and 6 RAM chips of 8KB each. (6+6.5)
  2. Develop a program for Z80 to copy the elements of an array into an overlapping array.

 

 

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Loyola College M.Sc. Physics Nov 2006 Classical Mechanics Question Paper PDF Download

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                        LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

M.Sc. DEGREE EXAMINATION – PHYSICS

AC 14

FIRST SEMESTER – NOV 2006

PH 1809 – CLASSICAL MECHANICS

 

 

Date & Time : 02-11-2006/1.00-4.00    Dept. No.                                                       Max. : 100 Marks

 

 

PART A                      ( 10×2 = 20)

  1. What are cyclic coordinates? Show that the momentum conjugate to a cyclic coordinate

is a constant

  1. Give an example of a velocity dependent potential
  2. State and express Hamilton’s variational principle.
  3. What are Euler’s angles?.
  4. Show that the kinetic energy T for a torque free motion of a rigid body is

a constant of motion.

  1. What is meant by canonical transformation?
  2. Show that the generating function F4 = pP generates a transformation that interchanges

momenta and coordinates.

  1. Show that [q,H]q,p = q dot and [p,H]q,p = p dot
  2. Express the Hamiltonian using Hamilton’s characteristic function W in polar coordinates

for a particle under a central force V(r).

  1. Define action variable J and angle variable w.

 

PART B                     (4×7.5 = 30)

Answer any Four questions only

11a Establish the relation between the Lagrangian and the Hamiltonian   (4 marks).

b.Obtain the equations of motion of a simple pendulum using the Hamiltonian formulation.

(3.5 marks)

  1. Obtain Hamilton’s equations of motion from the variational principle.
  2. Solve the equation of orbit given : q = l ò   dr/r2   / [2m (E+ V(r) – l2/2mr2 ]½    +   q’

for an attractive central potential and classify the orbits in terms of e and E.

14a Obtain the tranformation equation for the generating function F2(q,P,t)    (4.5 marks)

b Show that the transformation Q = q +  ip and P = q – iP is not canonical   (3marks)

  1. Solve the harmonic oscillator problem by the HJ method.

 

PART C                     (4×12.5 = 50)

Answer any Four questions only

16a. Derive the general  form of Lagrange’s equation using D’Alembert  principle.  (8 marks)

  1. A particle of mass m moves in one dimension such that it has the Lagrangian

L = m2x4/12 + mx2V(x) –V2(x) where V is some differentiable function of x. Find the

equation of motion for x.           (4.5 marks)

17a. Obtain Euler’s equations of  motion for rigid body acted upon by a torque N  (6 marks)

  1. Solve the Euler’s equation of motion for a symmetric top I1=I2 ≠ I3 with no torque

acting on it                                                                                  (6.5 marks)

18a. Show that the Poisson bracket is invariant under canonical transformation  (8 marks)

  1. Prove that an infinitesimal canonical transformation does not change the value of the

Hamiltonian of a system.   (4.5 marks)

  1. Solve the Kepler’s problem in action-angle variables.
  2. Write notes on any TWO of the following
  3. i) Constraints of motion
  4. ii) Coriolis Effect

iii)  Hamilton Jacobi method.

 

 

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Loyola College M.Sc. Physics Nov 2007 Relativity And Quantum Mechanics Question Paper PDF Download

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Loyola College M.Sc. Physics April 2008 Statistical Mechanics Question Paper PDF Download

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

FG 28

M.Sc. DEGREE EXAMINATION – PHYSICS

FIRST SEMESTER – APRIL 2008

    PH 1810 / 1801 – STATISTICAL MECHANICS

 

 

 

Date : 05/05/2008            Dept. No.                                        Max. : 100 Marks

Time : 1:00 – 4:00

PART A ( 20 MARKS )

ANSWER ALL QUESTIONS. Each question carries 2 marks.

 

  1. State the ergodic hypothesis. Is it true ?
  2. Distinguish between the micro-canonical ensemble and the canonical ensemble.
  1. State the postulate of equal-a-priori probability.
  1. Sketch the Maxwell velocity distribution
  2. How does the vibrational contribution to the specific heat vary with temperature ?
  3. What are quasi-particles ? Give an example.
  4. What is the pressure exerted by an ideal Fermi gas at absolute zero ?
  5. What is the importance of the Chandrasekhar limit ?
  6. What is the implication of Einstein’s result for the energy fluctuations of blackbody radiation ?
  7. State Nyquist theorem.

 

    PART B ( 30 MARKS )

ANSWER ANY FOUR QUESTIONS. Each question carries 7.5 marks.

 

  1. State and explain the basic postulates of statistical mechanics.
  2.  Obtain the distribution for an ideal Maxwell –Boltzmann gas.
  3.  Explain Bose-Einstein condensation. Discuss the super-fluidity of Helium by considering it as a form of Bose-Einstein condensation.
  4. Derive the Richardson-Dushman equation, which describes thermionic emission.
  5.  Obtain the relations, which state the Wiener-Khintchine theorem.

 

PART C ( 50 MARKS )

ANSWER ANY FOUR QUESTIONS. EACH QUESTION CARRIES 12.5 MARKS.

 

  1. (a)  Explain Gibb’s paradox. How is it resolved ?

(b) Prove Liouiville theorem.

  1. Calculate the entropy of an ideal  Boltzmann gas  using the micro canonical ensemble. Explain the corrections to be made to obtain the Sackur-Tetrode equation.

 

  1.   Discuss the thermodynamic properties of an ideal Bose-Einstein gas.

 

  1.  Calculate the pressure exerted by a Fermi-Dirac gas of relativistic electrons in the ground state. Use the result to explain the existence of the Chandrasekhar limit on the mass for a white dwarf.
  2.  (a) Calculate the concentration fluctuations for a grand canonical ensemble. Show that for an ideal classical gas it increases as the volume of the gas increases.

(b)   Prove the Nyquist theorem.

 

 

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Loyola College M.Sc. Physics April 2008 Relativity And Quantum Mechanics Question Paper PDF Download

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

FG 36

M.Sc. DEGREE EXAMINATION – PHYSICS

THIRD SEMESTER – APRIL 2008

    PH 3808 – RELATIVITY AND QUANTUM MECHANICS

 

 

 

Date : 29/04/2008            Dept. No.                                        Max. : 100 Marks

Time : 9:00 – 12:00

PART A                                         (10 x 2m =20m)

Answer ALL questions

 

  1. Distinguish between timelike and spacelike
  2. Write down the Lorentz transformation equations between the proper velocities in two inertial frames for a boost along the common x-axis.
  3. How does charge density transform under Lorentz transformation?
  4. What is 4-potential in relativistic electromagnetism?
  5. What is a Green’s function?
  6. What is screened Coulomb potential?
  7. Distinguish between first and second order transitions of the time dependent perturbation theory with the help of schematic diagrams.
  8. What is dipole approximation in emission/absorption process of an atom?
  9. What is the limitation of Klein-Gordon equation?
  10. Write down the four Dirac matrices?

 

PART B                                       (4 x 7 1/2m= 30m)

Answer any FOUR questions

 

  1. a) If a particle’s kinetic energy is equal to its rest mass energy, what is its speed?
  2. b) Obtain the relation between the relativistic energy and momentum. (3 ½ +4)
  3. Explain how the components of magnetic field transform as viewed from another inertial frame.
  4. Outline the wave mechanical picture of scattering theory to obtain the asymptotic form of the wave function in terms of scattering amplitude.
  5. Obtain an expression for the transition amplitude per unit time in the case of Harmonic perturbation.
  6. Write down the Dirac matrices in terms of Pauli spin matrices and establish their anticommuting properties.

PART C                                     (4 x 12 1/2m = 50m)

    Answer any FOUR questions

 

  1. (a) Discuss the work-energy theorem in relativity.

(b) The coordinates of event A are ( x A, 0, 0, t A) and the coordinates of event B

are ( x B, 0, 0, t B). Assuming the interval between them is time like, find the

velocity of the system in which they occur at same place.

  1. Establish the covariant formulation of Maxwell’s equations.
  2. Discuss the Born approximation method to obtain an expression for the scattering amplitude
  3. Discuss the time evolution of quantum mechanical problem in the case of constant perturbation and obtain the Fermi’s Golden rule.
  4. Obtain the plane wave solutions and the energy spectrum of the Dirac equation.

 

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Loyola College M.Sc. Physics April 2008 Quantum Mechanics Question Paper PDF Download

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

M.Sc. DEGREE EXAMINATION – PHYSICS

FG 30

SECOND SEMESTER – APRIL 2008

PH 2808 – QUANTUM MECHANICS

 

 

 

Date : 22/04/2008            Dept. No.                                        Max. : 100 Marks

Time : 1:00 – 4:00

PART A                                               (10 x2 m = 20 m)

 

  • Prove that the momentum operator is self adjoint.
  • In what way is the orthonormal property of eigenfunctions belonging to discrete set of eigenvalues different from those of continuous set?
  • Define parity operator. What is its action on a wave function ψ ( r, θ, φ)?
  • What is a rigid rotator and what are its energy eigenvalues?
  • Expand an arbitrary state vector in terms of certain basis vectors. Define projection operator.
  • Explain the term the ‘wave function’ of a state vector ׀ψ>.
  • Given that [ JX,JY] = iħ JZ and its cyclic, verify that [ J+, J–] = 2ħ JZ, where J+ = JX + iJY and J– = JX– iJY.
  • Prove that the Pauli spin matrices anticommute.
  • Write down the Hamiltonian of a hydrogen molecule.
  • Explain the terms classical turning points and the asymptotic solution in the context of WKB approximation method.

PART B                                            ( 4×7 ½ m = 30 m)

ANSWER ANY FOUR QUESTIONS

 

  • (a) Verify the identities [ AB, C) = A [ B, C] + [ A, C] B and [ A, BC] = B[A, C] + [ A, B] C . (b) Determine [ x2, p2], given that [ x, p] = iħ.
  • Evaluate ( um, x un) where un’s are the eigenfunctions of a linear harmonic oscillator.
  • Prove that “the momentum operator in quantum mechanics is the generator of infinitesimal translations”.
  • (a) Prove that ( σ.A) (σ.B) = B + i σ. ( A xB) where σ’s are the Pauli spin matrices , if the components of A and B commute with those of σ. (b) Determine the value of (σx +i σy)2.
  • Estimate the ground state energy of a two-electron system by the variation method.

PART C                                          ( 4x 12 ½ m=50 m)

ANSWER ANY FOUR QUESTIONS

 

  • (a) State and prove closure property for a complete set of orthonormal functions. (b) Normalize the wave function ψ(x) = e – ׀x׀
  • Discuss the simple harmonic oscillator problem by the method of abstract operators and obtain its eigenvalues and eigenfunctions.
  • (a) The position and momentum operators xop and pop have the Schrödinger representations as x and –iħ ∂/∂x”-Verify this statement.(b) Explain the transformation of Schrödinger picture to Heisenberg picture in time evolution of quantum mechanical system.
  • Determine the eigenvalue spectrum of the angular momentum operators J2, Jz ,J+ and J–, starting with the postulate [ Jx, Jy] = iħ Jz and its cyclic.
  • Outline the perturbation theory of degenerate case with specific reference to the two-dimensional harmonic oscillator.

 

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Loyola College M.Sc. Physics April 2008 Quantum Mechanics – I Question Paper PDF Download

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

FG 47

M.Sc. DEGREE EXAMINATION – PHYSICS

SECOND SEMESTER – APRIL 2008

    PH 2806 / 2801 – QUANTUM MECHANICS – I

 

 

 

Date : 03/05/2008            Dept. No.                                        Max. : 100 Marks

Time : 1:00 – 4:00

                                    PART A ( 10 X 2 = 20 MARKS )

ANSWER ALL QUESTIONS. EACH QUESTION CARRIES 2 MARKS.

 

  1. What is meant  by classical approximation in wave mechanics ?
  2. Can classical concepts explain the Compton effect ?
  3. Define probability density and probability current density.
  4. What are stationary states ?
  5. What is an observable ? Give an example.
  6. State the expansion postulate.
  7. Sketch the first two wave functions of the stationary states of a simple harmonic oscillator.
  8. What are coherent states ?
  9. What is the effect of an electric field on the energy levels of an atom ?
  10. What is the origin of the exchange interaction ?

 

 

PART B ( 4 X 7.5 = 30 MARKS )

ANSWER ANY FOUR QUESTIONS. EACH QUESTION CARRIES 7.5 MARKS.

 

  1. State and explain the uncertainity principle.
  2. (a) Explain Born’s interpretation of the wave function.

(b) Explain the significance of the equation of continuity.

  1. (a) Explain the principle of superposition.

(b) Explain the property of closure.

  1. Solve the eigenvalue equation for L 2 by the method of separation of variables.
  2. Explain the use of perturbation theory for the case of a 2-d harmonic oscillator.

 

PART C ( 4 X 12.5 = 50 MARKS )

ANSWER ANY FOUR QUESTIONS. EACH QUESTION CARRIES 12.5 MARKS.

 

  1. Describe Compton effect and derive an expression for the shift in wavelength of the scattered beam.

17.Consider a square potential barrier on which is incident a beam of particles of energy E. Calculate the         reflected intensity and transmitted intensity, if the barrier height is V and width is a.

  1. (a) Discuss the eigenvalue problem for the momentum operator.

(b) Discuss the postulate regarding evolution of a system with time.

  1. Obtain the Schrodinger equation for a linear harmonic oscillator and find its eigenvalues and

eigenfunctions.

  1. Discuss the WKB approximation method of solving eigenvalue problems. Consider the 1-d case and

find the solution near a turning point.

 

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