LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
B.Sc. DEGREE EXAMINATION – PHYSICS
SIXTH SEMESTER – April 2009
PH 6605 - QUANTUM MECHANICS & RELATIVITY
Date & Time: 27/06/2009 / 10:00 - 1:00 Dept. No.
PART A
Answer all questions. All questions carry equal marks.
Max. : 100 Marks
(10 x 2 = 20 marks)
1. Define photoelectric effect and write the photoelectric equation.
2. State Heisenberg uncertainty principle.
3. State Ehrenfest theorem?
4. Give physical interpretation of wave functions.
5. Define a Hermitian operator. Give an example.
6. Prove [ L2, Lz] = 0 [Lz, L+] = ±ħL±.
7. Distinguish between inertial and non-inertial frames of references.
8. State the postulates of special theory of relativity.
9. State principle of equivalence.
10. The time interval as measured by an observer at rest is 2.5 x 10-8s . What is the time interval
as measured by an observer moving with velocity v =0.73c?
PART B
Answer any four questions.
(4 x 7.5 = 30 marks)
11. Calculate the de-Broglie wavelength for electrons and protons if their speed is 105 m/s..
12. A one dimensional harmonic oscillator moves in a potential of v(x)= ½ mw2x2. Separate the
schroedinger equation and show that the allowed energies are given by E = (n+1/2)ħω..
13. Prove that the Eigenvalues of a Hermitian operators are real and the Eigenfunctions
corresponding to the distinct eigenvalues are orthogonal.
14. Derive Einstein’s mass energy equation.
15. Explain the Gravitational Red-shift.
PART C
Answer any four questions.
(4 x 12.5 = 50 marks)
16. Draw a neat sketch of an electron microscope and explain its working.
17. Obtain the transmission coefficient for a potential barrier.
-∞ ≤ x < 0
E< V
0 ≤ x < a
E= V
x > a
E> V
18. Calculate the energy of a hydrogen atom by solving the Schrodinger equation in spherical
polar coordinates.
19. Discuss in detail the Michelson – Morley experiment. Give possible explanation for the null
result.
20. a) What is the importance of Mach’s principle?
b) Explain briefly any one experiment that lends support to Einstein’s theory of gravity?
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