DISTANCE EDUCATION
M.Sc. DEGREE EXAMINATION, MAY 2016.
Physics
QUANTUM MECHANICS
(2008 onwards)
Time Three hours Maximum 100 marks
Answer any FIVE questions.
Each question carries 20 marks.
20 100)
1. Explain the wave particle duality.
Derive the time dependent schroidinger's wave
equation. Deduce the time independent wave
equation from it for the stationary states.
Derive the equation of continuity and from that
equation give interpretation for current density and
position probability density.
2. State Heisenberg's uncertainty principle.
Derive a mathematical proof of the position
momentum uncertainty relation.
Explain elaborately the quantum mechanical
tunneling problem.
Write a note on Schwartz inequality.
Sub. Code
22
DE-3837
2
Wk 16
3. Explain time independent perturbation theory for
non degenerate level.
Explain the first order stark effect in Hydrogen
atom.
Define parity operator and projection operator.
4. Solve the radial part of Hydrogen atom.
Derive the solution for schrodinger's wave equation
for rigid rotator.
5. Describe Dirac's bra and ket vector notations.
Elaborate W.K.B. approximation.
Distinguish Raman and Rayleigh scattering.
6. Prove
x ,Px i and
Px
m i
x H

Where x Px H
are position, momentum and
Hermitian operators.
Discuss the scattering problem using the Born
approximation and get an expression for the
scattering Cross section.
Distinguish spontaneous emission and stimulated
emission.
7. Give the time dependent perturbation theory and
get an expression for Fermi's golden rule.
Explain diffusion scattering.
Obtain the relation between Einsteins A and B
coefficients.
DE-3837
3
Wk 16
8. Describe the method of partial waves for the
scattering process.
Prove 0

where L

is the angular momentum
operator.
Define C.G. coefficients. Discuss the construction
procedure for the C.G. coefficient matrix.