Bharathiar University 2003 M.Sc Physics Quantum Mechanics-II - Question Paper
Degree
S,g No, t.............................
(For the candidates admitted from 2002 and onwards) M.Se, DEGK1E EXAMINATION, APRIL 2003. Second Semester Physics
Time : Three hours ...... Maximum : 100 marks
SECTION A (20 x 1 = 20 marks)
Answer ALL questions.
Choose the correct answer :
1. The relationship between scattering amplitude fX9t<j>) and scattering cross-section o#sf) is
(a)
m
(c)
2, The energy levels of a multi electron atom depend
upon
(c) Both n and I - _
(d) Neither n aor I, ' *
3, Landes splitting factor g for s electron is
(a) 0
(c) 1
4. v Let An and Btl be Einsteins coefiiuienU then tbs field density uu is given by
|
(a) -1 |
 |
 |
|
<d) |
2
The aimihilatioa operator for the state K is
0 0 0 0
1 0 0 0 .
0 42 0 0 -
(a)
0.0 0 ...
0 vi 0 0
0 0 I 0
O' 0 0 3
(b) . aK
0 0 0 0
Vi G 0 0
0 2 n 0
0 0/3 0
0 0 0 0
0 0 0 0
0 t/T 0 0
0 0 2 0
o o o'.
(c)
Ur =
( nx =
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Fill up the blacks:
6. The Bora approximation simply amounts neglecting lie rescattering of the'scattered waves provided--,
7.- Hartree assumed that the electrons in a multi electron atom move independently in a--
8. In covalent bending one or more pairs of electrons are --- by the two atoms.
9. The transition probabilities of----
and --- are the same.
10. A physical system having infinite degrees of freedom is ealkd a -. . .
Match the following:
11. Scattering cross-section (a) Hydrogen molecule
12. Self-consistent :le!d (b) Dirac
13. Covalent bond (c) Hartree
14. Transition probability (d) Bam
15. Fie'd quantization ' (e) Einstein.
n 'i
Answer in 1 or 2 sentences ;
17. What is meant by doublet separation in all " spectra?
18. What is meant tjT CpiXfc Cl Interaction?
19. Why is the theory , of radiation considered semi-classical? .
20. What is a number operator?
SECTION B (5 x 8 = 30 aarks)
Answer ALL qisstions* choosing vLLl.4 vi Co).
21. (a) Explain the terms differential scattering , cross-section, total scattering cross-section and
Or
(b) Write a note on phase shifts m partial wave analysis. , '
22. (a) -What is meant by central field approximation?
(b) Explain, briefly Hartrea-Pods etpafioa.
23. (a) Discuss briefly spin-orbit interaction as a correction to central field approximation.
Or
(b) Explain hybridisation with an example,
24, (a) What are Einstein's coefficients?
Or
(b) Write a note on density matrix.
25, (a) Wht is meant by qtj?n%a#in of wave fields?
Or
ib) Derive the quantum equation of the field,
Answer ALL questions, dioosiag either (a) or Co).
26, (a) Give 111 theory of Bora /approximation and discuss the conditions . for the validity of Bora approximation.
(b) Describe fully the method of partial waves for scattering.
27, (a) Discuss fully Biomas-Feiml statistical model to determine the potential energy in the central field approximation.
Or
(b) Obtain the central fiilS approximation using Hartrees self-consistent field method. Compare this method with Tbomm-Femii statistical model,
28,- (a) Explain in detail Heitler-London theory to ootain the energy values of the hydrogen molecule
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(b) Explair xiJly Hartree-Fock self-consistent field method for a molecule.
29. (a) Derive expressions for. the transition probabilities per mat time for absorption and induced ' emission using perturbation theory.
Or
(b) Discuss the interaction of m atom with electromagnetic radiation and find an expression for the transition probability.
30. (a) Discuss the classical formulation of Lagrangian and Hamiltonian equations of motion.
- Ur
(b) Explain fully the quantisation of non-relativistic Scarodmger equation.
8,
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i
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Attachment: |
| Earning: Approval pending. |
