DISTANCE EDUCATION
M.Sc. (Physics) DEGREE EXAMINATION, DECEMBER 2017.
QUANTUM MECHANICS
(2008 onwards)
Time Three hours Maximum 100 marks
Answer any FIVE questions.
Each questions carries 20 marks. x 20 100)
1. Derive time independant Schrodinger equation.
Explain the physical interpretation of wave function
and normalisation of wave function.
Obtain the energy Eigen values and Eigen functions
for the linear harmonic oscillator.
2. Develop the Schrodinger equation for hydrogen
atom problem and separate the radial part of the
equation.
Solve the radial part of the Schrodinger equaiton for
hydrogen atom problem.
Discuss the degeneracy of the energy levels and
mention briefly the conditions under which the
degeneracy will be removed.
3. Derive the Schrodinger equation for a rigid
rotator.
Find the Eigen values and Eigen functions of the
rigid rotator.
Explain how the results of the rigid rotator are used
to explain rotational spectrum of diatomic
molecule.
Sub. Code
22
DE-2957
2
WK 16
4. Discuss the variational methods to solve
Schrodinger equation.
Solve the Schrodinger equation to find the energy of
the ground state of helium atom.
5. What do you understand by stimulated emission of
radiation? Explain.
Discuss about Einstein's A and B coefficients.
Calculate Einstein's coefficients by perturbation
theory.
6. Explain Schwartz inequility.
Discuss about unitary and projection operators.
Explain the Stark effect in the ground state of
hydrogen atom.
7. What do you understand by scattering cross section?
Deduce an expression for scattering cross section of
particle using a spherically symmetic potential.
Distinguish between Rayleigh and Raman
scattering.
Explain Born approximation, obtain the condition
for the validity of Born approximation.
8. Outline the method of addition of two angular
momenta.
Evaluate the Clebsch Gordan coefficients for two
spin ½ particles.
Obtain the recursion relation for Clebsch Gordon
coefficients.