Bharathiar University 2001 M.Sc Physics Quantum Mechanics -II - Question Paper
Degree
(For the candidates admitted from 109 onwards) M.Sc. DEGREE EXAMINATION NOVEMBER 2001.
. Seventh Semester
Physics
QUANTUM MECHANICS II
Time. : Three hours Masmaa 1100 marks
SECTION A - (10 x 2 = 20 marks)
Answer ALL questions.
Choose the correct answer :
2. A suitable Hamiltonian H which takes into account the mutual interactions of the electrons as well as spin, erMt iataction is *
i-i ,2m , n i tiru
H _ j "{j
|
(c) |
H-'S* |
r . q bL | |
|
jLd i 1 |
[2m | ||
|
(d) |
H-t 1 |
[2m |
+" _ |
ze
-2
3. The spectroscopic value for the Marandear distance for H-molecule is
* > "(c) 0.74 A0 id- 0.002 A
4. If p* is density matrix and F is any operator then (#) fe
(a) Trace |jj
c Trace (p)
fFl
P
\
(c) Trace
5. Lagrangian equation for the generalised co-ordinate ai iz,
d,
i i/ Ml]
3 a,. dtl 3of
(c)
= 0.
|
= 0 | |||||||||
|
(d) |
| ||||||||
Answer ALL questions in 1 or 2 sentences :
6. Give the connecting relation between scattering amplitude and cross section.
7. What is the type of atoms for which Thomas Fermi method is suited to?
8. Give the meaning ofself-consistent*,
1
9. Her.* will you spin --density matrix?
1, Define Hermiatiaa operator Nk through creation
' operator oA and annihilation operator a*.
* 3 , 3048
11. (a) Show that the scattering amplitude f(, $)
bears a relation with scattering cross section
Or
(H'i In the neutron proton scattering, assuming that the range of the attractive force V to be approximately, 3 x 1CH3 cm, show that the scattering amplitude will be almost isotropic (in the centre of the mass system) for neutron energy < 10 MeV.
12. (a) What is the Poissons equation used in
't,
Thomas-Fenni statistical model to determine the potential? What are the boundary conditions for {r)?
Or .
(b) Write a note on doublet separation,
13. (aj What ar-s the trial wave functions assumed in
H* ion problems?
Or
(b) Give examples for covalent bonding.
4
14, (a) How does Plancks concept of black body* is connected with or "absorption of radiations by 'atoms' constituting die walls?
Or
(b) Give any two application of density matrix,
15, (a) If the Lagrangian V for a system where the single particle Hamiltonian is Hennitian is given by,
t 4 _ --t
I = -r* 2 wi)" u f > then what
* i *
are the natures of L?
Or
(b> If af and S{ are generalised co-ordinates, what are the respective conjugate momentas valuer;? SECTION C (5x8 = 40 marks)
18. (a) Derive expression for the scattering
amplitude for the scattering by Yukawas potential,
!
Or
(b) Obtain suitable expression for the solution for
f for the seaUeringm terms of Green's functions,
5 3048
17. (a) Explain the principles involved in central field approximation,
(b) Discuss the coupling schemes. -*
IS, ' (a) la a Hydrogen like- atom, the spin orbit interaction is of the fonn
zm c r
since 2L-S *J2 -L2 -S3, choose ft representation in which J2,l? -and 8s are all well defined and calculate the spin orbit.correction. -
Or ~
(b) Give a detailed account on hybridisation.
19. (a) Discuss radiation field as. am assembly of oscillators. Obtain the selection rales. '
Or
(b) Deduce expression for the emission rate and absorption rate.
20. (a) Outline the properties of creation and destruction operators. Describe their commutation relations.
, ' ' Or (b) Obtain quantum equation fcr the field.
S10HON D (2 x 10 20 marks)
21. W Obtain expression for the free panicle solutk>a partial wave analysis. Also deduce expression for scattering amplitude.
... . Or
(b) scribe Bom's approximation to calculate the scattering amplitude f (ff, #),
22. (a) Obtain expression for the total energy .(symmetric <* antisymmetric) for the hychogen
molecd by Hotter London method.
(b) Calculate Einstein, Coefficient of induced emission and show that it is equal. to Einstein's coefficient absorption from semiclassica! theory of radiao'.
7 3048
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| Earning: Approval pending. |
