Bharathiar University 2001 M.Sc Physics Quantum Mechanics-I - Question Paper
Degree
iReg, No, s
(For the candidates admitted from 1999 and onwards) MLSe, DEGEEB'BJLAMINATION, APRIL 2001.
Second-Semester
? / '
Physics .
* h *
/ / ' ; '-''V ;
Time : Three hours".,' / / Mdmmhm.: 100 marks ,N / Answer ALL questions.
*
, j SECTION a (10 x 2* 20 marks)
1, If and a*- represent annihilation and creation operators then, the momentum operator p is,
(a) +o) ft) 'Ihw(f'r -d)
f
ls~ . s - e>
2, The most generai solution for WKB approximation is given by
(a) y = f j2irJE ~ V) +-*e * f -F)
. VP * * VP *
(b)
Cc) y=e*f%/2wrfr+vj
j? 1 l'i
A /J*
A *
(d) **>v a
r- ] C <zb
3, {j, x J is given by v- , \
(a) % (b) % v 0
(c> 4 Cd) -ite.
Transition probability per tait tn
(a) t = |fpJffs_r (b) TjJ
(c) t = A?%; r W) r*-~-p,p'imf
2z ' ' ' M 1
5. - Dirac's spin macrix 4 is
|
6 If a~x, i? then what is the value c ox | |
|
? ; dxl */= |  |
 |
|
scattering amplitude are related? |
9. What is the eigen value for the operator J, ?
10. Write down Klem-Gordaa's rektivistic equations,
SECTION B (5 x 4 = 20 marks)
Answer ALL questions.
11.'~ (a) Bring * mi the distinctions between Schrodinger picture and Heisenberg picture.
Or
(b) Explain bra and ket vectors.
12. (a) Give the meaning of degeneracy. Give an example for a four fold degeneracy.
Or
(b) Outline the principle ox WKB approximation.
3 2228
|
(13, (a) Exp-lain harmonic perturbation. Or loj Bnefly outline the method of sudden approximation, 14. (a) Show that %x ,,]= ihLx. Or (b) Show that 0. r |
1?. {a) Discuss Helium atom problem on the basis of perturbation theory. Or / (W Obtain the solution for a particle in a slowly varying potential field by WKB method, QS: (a) Evaluate the perturbation parameter V by etihsidering first order time dependent perturbation Or |
|
15, (a) From KG. relativist equation, show that P(x,i3 does not represent probability density. \ vS Or A. o r (fa) State any two properties of Gamma matrices, SECTION C (5x8 = 40 marks) ' A' 'A '< 5 "" Answer ALL questions. 16. (a) Describe vrith necessary theory, the harmonic oscillator problem on the basis of matrix mechanics. Evaluate eigen energy. Or Cb) Obtaia equation of motion in Dirac's picture. Bring out its important features. V 2229 V>V* h* |
(b) Explain adiabatic approsmation. Calculate transition probability coefficient *an * for the same, <</ (iS,1 (a) If wm is an eigen function of Lt with eigen value mh then the function (Lx +iLyf is also an eigen function of Lt with eigen value (mj)k where v=0*12"-- .. _ Or Co) Show that the commutation rules are valid for the sum of two or any number of angular momenta. Discuss coupled representation, 20. (a) Explain probability deasity using Dirac's relativist equation. xt" n fy? Or CM Explain hcle theory. ' ,i |
' *,V
SECTION D (2 x 10 = 20 marks)
Answer ALL questions.
21. (a) Using Kronig-Peimy model, gi%e a detailed
mmnnt on periodic potential.
Or
Cb) Using perturbation theory, -discuss the problem of first- excited state of hydrogen atom in stark effect. Calculate energy values.
22. (a) Discuss the transition probability for harmonic perturbation using time dependent perturbation theory.
Or
(b) Obtain the eigen values of angular momentum operator J2 when operated over an eigen function yJnt .
,ig 5h 10-
IB1 -
|
Attachment: |
| Earning: Approval pending. |
