LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

M.Sc. DEGREE EXAMINATION – PHYSICS

THIRD SEMESTER – APRIL 2012

PH 3811/3808 – RELATIVITY AND QUANTUM MECHANICS

 

 

 

Date : 24-04-2012             Dept. No.                                        Max. : 100 Marks

Time : 1:00 – 4:00

PART – A

Answer ALL questions:                                                                                                       (10×2=20)

• Can two simultaneous events in one inertial frame take place at same location in another inertial frame? Explain your answer.
• Differentiate between conserved and invariant quantities with suitable example.
• What are the components of a current density 4-vector? Write down the equation of continuity in covariant form.
• Can you transform a pure magnetic field in one inertial frame of reference into a pure electric field in another inertial frame of reference or vice versa? – Reason out your answer.
• Define differential scattering cross section.
• Write down the radial part of the Schrödinger equation for central potential.
• Illustrate with figure the third order transition of the time dependent perturbation theory.
• What is the significance of the (harmonic) perturbation being incoherent?
• Write down the Dirac matrices in terms of the (2×2) Pauli spin matrices and unit matrix
• Explain briefly the significance of the negative energy states of the Dirac equation

 

PART – B

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

• Explain the space-time diagram of Minkowski space clearly bringing out the concepts of ‘your future’ and ‘your past’.
• Establish the invariance of B under Lorentz transformation.
• Outline the method of solving the radial Schrödinger wave equation in the asymptotic region.
• Discuss the time-dependent perturbation theory to obtain an expression for the amplitude of first order transition
• Establish the anticommuting properties of the Dirac matrices

 

PART – C

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

• a) What are the transformation laws for (a) the proper velocity and (b) the ordinary velocity.

1. b) The coordinates of an event A are ( 10,0,0), ct_A=15 and the coordinates of event B are (15,0,0),

ct_B = 5 .Find the velocity of another inertial system in which they occur at the same place.

• Establish the covariant formulation of Maxwell’s equations.
• Explain the Born approximation of scattering process and obtain an expression for the scattering amplitude in the case of spherically symmetric potential.
• Discuss the time evolution of a quantum mechanical system in the case of constant perturbation and obtain the Fermi’s Golden rule
• Set up the Dirac’s wave equation for a free particle. Obtain its plane wave solutions and the energy spectrum.

 

Go To Main page

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

M.Sc. DEGREE EXAMINATION – PHYSICS

THIRD SEMESTER – NOVEMBER 2012

PH 3811/3808 – RELATIVITY AND QUANTUM MECHANICS

 

 

Date : 03/11/2012            Dept. No.                                        Max. : 100 Marks

Time : 9:00 – 12:00

PART – A

Answer ALL questions:                                                                                                                    (10×2=20)

1. Obtain the relation between proper velocity and ordinary velocity.
2. If a particle of kinetic energy one-fourth its rest energy, what is its speed?
3. State the equation of continuity in electromagnetism in terms of the 4-current.
4. How does charge density transform under Lorentz transformation?
5. Define differential scattering cross-section.
6. What are partial waves?
7. What do you understand by a selection rule?
8. What is meant by first and second order perturbation?
9. What is a hole, with reference to a free Dirac particle?
10. The dimensions of Dirac’s matrices have to be even. Why?

PART – B

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

11. (a) Explain the salient features of Minkowski’s space time diagram. (b) A pion at rest decays into a muon and a neutrino. Find the energy of the outgoing muon, in terms of the two masses m_π and m_μ (assume m_ν = 0)                                                                                 (3 + 4.5)
12. If a point charge q is at rest at the origin in system S₀, what is the electric field of this same charge in system S, which moves to the right at speed v₀ relative to S₀
13. Outline the Green’s function method of obtaining a formal solution of a Schrodinger wave equation in scattering theory.
14. Develop the time dependent perturbation theory up to second order.
15. Explain how Klein-Gordon equation leads to positive and negative probability density.

PART – C

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

16. (a) Explain Compton’s scattering and find an expression for the change in wavelength of the scattered X-ray beam.  (b) Discuss the work-energy theorem in relativity.
17. Obtain the transformation equations among the components of electric and magnetic fields of the special theory of relativity.
18. Discuss the Born-approximation method of scattering theory and obtain an expression for the scattering amplitude.
19. Discuss the interaction of an atom with the radiation field and obtain an expression for probability in terms of energy density of the radiation field.
20. Obtain the plane wave solutions of the Dirac’s relativistic wave equation of a free particle.

Go To Main page