LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – PHYSICS

XC 23

SIXTH SEMESTER – April 2009

PH 6605 – QUANTUM MECHANICS & RELATIVITY

 

 

 

Date & Time: 18/04/2009 / 9:00 – 12:00      Dept.                                                         : 100 Marks

 

 

SECTION – A

 

Answer all the questions.                                                                                            (10×2 = 20 Marks)

1. State Heisenberg’s uncertainty principle. Give a mathematical form of the principle.
2. What is Compton effect?
3. Define probability current density.
4. What is tunnel effect?
5. Show that [ L_x, L_y ] = iħL_z.
6. Express the operator for angular momentum component L_x in spherical polar coordinates.
7. What are inertial and non – inertial frames of references?
8. At what speed is a particle moving if the mass is equal to three times its rest mass?
9. What is Mach’s principle?
10. State the postulates of General theory of relativity.

SECTION – B

Answer any four questions.                                                                                      (4×7.5 = 30 Marks)

11. (a) What is the principle of an electron microscope?                                                       (2)

(b)        Describe the working of an electron microscope with a diagram.                        (4+1.5)

12. Solve the Schrödinger equation for the linear harmonic oscillator and obtain its energy levels.                                                                                                                   (5.5+2)
13. (a) What is a Hermitian operator?                                                                                 (2.5)
    • Show that the eigen values of Hermitian operators are real. (5)
14. (a) Derive Einstein’s mass – energy relation.                                                                (5.5)
    • Explain mass – energy equivalence with two examples. (2)
15. Discuss planetary motion on the basis of Einstein’s theory of gravitation and interpret the path of the planet about the sun.           (7.5)

 

 

SECTION-C

Answer any four questions.                                                                           (4×12.5 = 50 Marks)

16. (a) What are matter waves? (2)

(b) Describe Davisson – Germer experiment to confirm the concept of matter waves.          (10.5)

17. Starting from the time dependent Schrodinger equation, obtain the time independent

Schrodinger equation.                                                                                                      (6.5+6)

18. Write down the radial part of the time-independent Schrödinger wave equation for the hydrogen atom and solve the equation to obtain the Eigen values of the energy of the atom. (10+2.5)
19. (a) Describe Michelson – Morley experiment and explain the physical significance of the

negative result.                                                                                                             (8+2.5)

(b) How fast would a rocket have to go relative to an observer for its length to be contracted

to 99% of its length at rest?                                                                                                 (2)

20. (a) Derive an expression for gravitational red shift. (6.5)

(b) Write a note on bending of light rays in a gravitational field.                                                (6)

 

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    LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

XC 21

B.Sc. DEGREE EXAMINATION – PHYSICS

SIXTH SEMESTER – April 2009

PH 6603 – QUANTUM MECHANICS & RELATIVITY

 

 

 

Date & Time: 18/04/2009 / 9:00 – 12:00          Dept. No.                                                    Max. : 100 Marks

 

 

                                                             PART – A

Answer ALL questions:                                                                                             (10×2=20 Marks)

 

1. What are the assumptions of Planck’s radiation law?
2. An electron is confined to a box of length 10^-10m.Calculate the minimum uncertainty in its

velocity.

3. What is a normalized wave function?
4. Express the potential function of a particle in a box of width ‘ ’ and of infinite height.
5. Explain the commutative property of operators with an example.
6. Write down the eigen value equation for L².
7. Show that acceleration is invariant in all inertial frames, according to classical relativity.
8. What is the velocity of π-mesons whose observed mean life is 2.5×10^-7s. The proper mean

life is  2.5×10^-8s.

9. What is principle of equivalence?
10. Explain the concept of gravitational lens.

PART – B

Answer any FOUR questions:                                                                          (4×7.5=30 Marks)

 

11. a) Explain de Broglie’s hypothesis of matter waves and derive an equation for the wavelength

of such waves.                                                                                                                         (4.5)

 

1. b) Calculate the de Broglie wavelength of waves associated with an electron which has been

accelerated from rest through a potential of 100V.                                                                   (3)

 

12. Calculate the energy levels of a particle in a one dimensional square well potential with

perfectly rigid walls.

 

13. Evaluate [x,P_x] and [L_x,L_y] (3.5+4)

 

14. a) Show that the length of an object appears to contract when moving with a velocity

comparable to that of light.                                                                                                     (5)

 

1. b) If the velocity of an object is 0.6c, find out the percentage of length contraction. (2.5)

 

15. Explain the basic ideas of general theory of relativity? Discuss the gravitational red shift

based on it.                                                                                                                              (3.5+4)

PART – C

Answer any FOUR questions:                                                                         (4×12.5=50 Marks)

 

16. a) Describe G.P.Thomson’s experiment to demonstrate the wave nature of electrons and

verify de Broglie’s hypothesis of matter waves.                                                                       (8)

 

 

4. b) Illustrate Heisenberg’s uncertainty principle with an example. (4.5)

 

17. a) Discuss the motion of a particle in a three dimensional box. Find the eigenvalues

and eigenfunctions.                                                                                                                   (9)

 

3. b) Explain non-degenerate and degenerate energy levels. (3.5)

 

18. Solve the Schrodinger’s equation for a hydrogen atom.

 

19. a) Derive the equations of Lorentz transformation. (10)

 

2. b) The total energy of a particle is exactly twice its rest energy. Calculate its speed. (2.5)

 

20. Discuss the following experimental observations which support general theory:

(i) Planetary motion and (ii) bending of light.                                                                        (6.5+6)

 

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – PHYSICS

SIXTH SEMESTER – APRIL 2011

PH 6609/ 6605/6603/6600 – QUANTUM MECHANICS & RELATIVITY

 

 

 

Date : 05-04-2011              Dept. No.                                        Max. : 100 Marks

Time : 9:00 – 12:00

 

PART – A

Answer ALL the questions.                                                                                   (10 × 2 = 20 Marks)

1. What are de Broglie waves?
2. Mention any two applications of an electron microscope.
3. What is the physical interpretation of wave function?
4. Calculate the minimum energy of an electron in an infinitely deep potential well of width 4nm. Given that h=6.625×10^-14Js and mass of the electron is 9.11×10^-31
5. What is meant by zero point energy in quantum mechanics?
6. Show that [x,p] = i ħ.
7. What is the conclusion from the results of Michelson-Morley experiment?
8. What is the fundamental importance of mass-energy relation in nuclear physics?
9. State two postulates of general theory of relativity.
10. Distinguish between inertial mass and gravitational mass.

 

PART – B

Answer any FOUR questions.                                                                                    (4 × 7.5 = 30 Marks)

11. (a) State and explain the uncertainly principle.                                                            (4)

(b)  An electron has a speed of 4×10⁵ms^-1 accurate to 0.01%.  With what fundamental

accuracy can we locate the position of electron?

Given mass of electron = 9.11×10^-31kg.                                                                     (3.5)

12. Explain the theory of α- disintegration using the tunnelling effect in quantum mechanics.
13. Obtain the expressions for orbital angular momentum operator in both Cartesian and Spherical polar coordinates. (3+4.5)
14. Write notes on: (i) Length contraction                                                                         (4)

(ii)    Time dilation                                                                                       (3.5)

15. Discuss the bending of light rays in a gravitational field.

 

PART – C

Answer any FOUR questions.                                                                                    (4× 12.5 = 50 Marks)

 

16. (a) Describe G.P Thomson’s experiment on electron diffraction and explain the

important conclusions.                                                                                                     (10)

(b) What voltage must be applied to an electron microscope to produce electrons of

wavelength 0.40A?                                                                                                            (2.5)

17. Derive Schrödinger’s time independent and time dependent wave equations using the

concept of matter waves.                                                                                                    (7.5+5)

18. Solve the radial part of the time independent Schrödinger wave equation for the

hydrogen atom and hence obtain the energy levels of the hydrogen atom.   (10+2.5)

19. (a) Derive the expression for the relativistic variation of mass with velocity. (10)

(b)  A proton of rest mass 1.67×10^-27kg is moving with a velocity 0.9c.

Find its mass.                                                                                                                      (2.5)

20. (a) Write a note on gravitational red shift.      (6.5)

(b) Explain planetary motion using Einstein’s theory of gravitation.                                            (6)

 

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – PHYSICS

SIXTH SEMESTER – APRIL 2012

PH 6609/PH 6605/6003/6600 – QUANTUM MECHANICS & RELATIVITY

 

 

 

Date : 16-04-2012              Dept. No.                                        Max. : 100 Marks

Time : 1:00 – 4:00

 

SECTION – A

Answer ALL the questions:                                                                       (10 × 2 = 20 Marks)

1. Mention the important properties of de Broglie waves.
2. What are the important applications of an electron microscope?
3. Give the physical significance of the wave function.
4. What do you mean by tunneling through a potential barrier?
5. What is Hermitian operator?
6. Show that [L_x, L_y] = i ħ L_z.
7. What will be the speed of a photon in one reference frame if it moves with a speed c in another frame of reference?
8. Calculate the rest mass energy of an electron in eV.
9. State Mach’s principle.
10. State the principle of equivalence.

 

SECTION – B

Answer any FOUR questions:                                                                             (4 × 7.5 = 30 Marks)

11. (a) Distinguish between optical microscope and electron microscope.                                      (5)

(b)  Calculate de-Broglie wavelength associated with a proton moving with (1/30)c

(h= 6.62 × 10^-34Js and m = 1.67×10^-27kg).                                                                       (2.5)

1.  (a) Write down Schrödinger equation and eigen values for a linear harmonic

oscillator.                                                                                                                             (2+2)

(b)  Discuss zero point energy.                                                                                                  (3.5)

13. (a) What do you mean by eigen functions and eigen values?                                            (1.5+1.5)

(b)  Prove that every eigen value of Hermitian operator is real.                                                (4.5)

14. On the basis of Lorentz transformations discuss (i) length contraction and (ii) time dilation.                                                                                                                               (4+3.5)
15. (a) What do you mean by inertial mass and gravitational mass?                                    (1.5+1.5)

(b)  Discuss the Red shift of spectral lines in a gravitation field.                                             (4.5)

 

SECTION – C

Answer any FOUR questions:                                                                      (4× 12.5 = 50 Marks)

 

16. (a) Describe, with neat diagrams, the experiment of Davisson and Germer on the

diffraction of electrons to establish the wave nature of matter.                                         (10)

(b)   If the uncertainty in the location of a particle is equal to its de Broglie wavelength,

What is the uncertainty in its velocity?                                                                             (2.5)

 

17. Solve the Schrödinger equation for a particle moving in one dimensional potential well

of finite depth to find eigen functions and eigen values.

 

18. Solve the radial part of Schrödinger equation for the hydrogen atom to obtain eigen

values of energy.

 

19. Describe the Michelson-Morley experiment and discuss the various interpretations for

the negative result of the experiment.                                                                                    (10+2.5)

 

20. Discuss the motion of a planet in the gravitational field of the sun and explain the

advance of the perihelion of Mercury.                                                                                   (8+4.5)

 

 

 

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