LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
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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
- Distinguish between timelike and spacelike
- Write down the Lorentz transformation equations between the proper velocities in two inertial frames for a boost along the common x-axis.
- How does charge density transform under Lorentz transformation?
- What is 4-potential in relativistic electromagnetism?
- What is a Green’s function?
- What is screened Coulomb potential?
- Distinguish between first and second order transitions of the time dependent perturbation theory with the help of schematic diagrams.
- What is dipole approximation in emission/absorption process of an atom?
- What is the limitation of Klein-Gordon equation?
- Write down the four Dirac matrices?
PART B (4 x 7 1/2m= 30m)
Answer any FOUR questions
- a) If a particle’s kinetic energy is equal to its rest mass energy, what is its speed?
- b) Obtain the relation between the relativistic energy and momentum. (3 ½ +4)
- Explain how the components of magnetic field transform as viewed from another inertial frame.
- Outline the wave mechanical picture of scattering theory to obtain the asymptotic form of the wave function in terms of scattering amplitude.
- Obtain an expression for the transition amplitude per unit time in the case of Harmonic perturbation.
- 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
- (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.
- Establish the covariant formulation of Maxwell’s equations.
- Discuss the Born approximation method to obtain an expression for the scattering amplitude
- Discuss the time evolution of quantum mechanical problem in the case of constant perturbation and obtain the Fermi’s Golden rule.
- Obtain the plane wave solutions and the energy spectrum of the Dirac equation.
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