M.Sc. DEGREE EXAMINATION, APRIL 2016
Second Semester
Physics
QUANTUM MECHANICS — I
(2011 onwards)
Time 3 Hours Maximum 75 Marks
Section A (10 2 20)
Answer all questions.
All questions carry equal marks.
1. What is known as wave-particle duality?
2. Can we write the uncertainty relation with two position
variables? Justify.
3. What is called a central potential?
4. What are spherical harmonics?
5. What are the limitations of perturbation theory?
6. When does WKB method fail?
7. What are the conditions for stimulated emission to occur?
8. Mention the semiclassical limit of radiation theory.
9. What is called scattering amplitude?
10. When does Born approximation fail?
Sub. Code
521201
RW-10844
2
Sp 1
Section B 5 25)
Answer all the questions.
All questions carry equal marks.
11. Derive the time-dependent Schroedinger equation.
Or
Verify whether the eigen-functions
Acoskx, Bsinkx of a particle
in a box, are orthogonal.
12. Treating as a rigid rotator, obtain the rotational
energy spectrum of a hydrogen molecule.
Or
Derive the radial Schroedinger equation.
13. Discuss the non-degenerate first-order perturbation
theory.
Or
Apply the WKB approximation to a one-dimensional
harmonic oscillator and obtain the energy spectrum.
14. Discuss Einstein's theory of radiation for a two-level
system and mention the significance of the results.
Or
Briefly discuss the quantum theory of radiation
within the frame-work of time-dependent
perturbation theory.
15. Discuss the theory of scattering using the Born
approximation.
Or
Discuss briefly the theory of scattering by screened
Coulomb potential.
RW-10844
3
Sp 1
Section C 10 30)
Answer any three questions.
All questions carry equal marks.
16. Discuss the theory and results of a one-dimensional
harmonic oscillator.
17. Deduce the bound state energy spectrum of hydrogen
atom.
18. Applying variational method, deduce the energy
spectrum of a deuteron.
19. Explain the phenomenon of Rayleigh scattering using
time-dependent perturbation theory.
20. Discuss the general theory of partial wave analysis in
scattering.