N A L A N D A O P E N U N I V E R S I T Y
M.Sc. Physics, Part-I
PAPER-II
(Quantum Mechanics)
Annual Examination, 2017
Time 3 Hours. Full Marks 80
Answer any Five Questions.
All questions carry equal marks.
1. Obtain expressions for the group velocity and the phase velocity of a de Broglie wave.
2. State Ehrenfest's theorem and show that classical mechanics agrees with quantum mechanics
so far as the expectation values are concerned.
3. Calculate the reflection and the refraction coefficients when a charged particle is incident from
the left with energy on a square well potential given by
4. Prove that momentum operation is self-adjoint.
Find the commutation relations of components of angular momentum.
5. Starting with momentum-position uncertainty obtain
6. Find the energy levels and energy eigenfunctions of a particle of mass m moving in a potential
7. Present the quantum mechanical theory of H-like atoms and discuss its energy level diagram
in relation to potential.
8. On the basis of WKB method discuss the case of one-dimensional harmonic oscillor and show
that the theoretical results match with exact results.
9. Discuss the scattering of particles by a spherically symmetric potential. Explain partial waves
and phase shift.
10. State and explain Fermi's golden rule. What do you understand by adiabatic and sudden
approximation