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

 

11. a) If a particle’s kinetic energy is equal to its rest mass energy, what is its speed?
12. b) Obtain the relation between the relativistic energy and momentum. (3 ½ +4)
13. Explain how the components of magnetic field transform as viewed from another inertial frame.
14. Outline the wave mechanical picture of scattering theory to obtain the asymptotic form of the wave function in terms of scattering amplitude.
15. Obtain an expression for the transition amplitude per unit time in the case of Harmonic perturbation.
16. 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

 

16. (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.

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

 

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

CC 25

M.Sc. DEGREE EXAMINATION – PHYSICS

THIRD SEMESTER – November 2008

    PH 3808 – RELATIVITY AND QUANTUM MECHANICS

 

 

 

Date : 05-11-08                 Dept. No.                                        Max. : 100 Marks

Time : 9:00 – 12:00

PART A                                                               (10 x 2 =20 marks)

Answer ALL questions

1. Distinguish between timelike and spacelike
2. Define proper velocity and ordinary velocity and state the relation between them.
3. Give the covariant form of Lorentz force equation.
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 Dirac matrices in terms of the (2×2)  Pauli spin matrices and unit matrix

 

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

Answer any FOUR questions

 

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

 

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

Answer any FOUR questions

 

16. (a) Explain the structure of space-time (Minkowski) diagram and bring out its

salient features.

(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 space- like, find the

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

 

17. Establish the covariant formulation of Maxwell’s equations.
18. Discuss the Born approximation method to obtain an expression for the scattering amplitude
19. Discuss the time evolution of a quantum mechanical system in the case of constant perturbation and obtain the Fermi’s Golden rule.
20. Set up the Dirac’s wave equation . Obtain its plane wave solutions and the energy spectrum.

 

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