Bharathiar University 2000 M.Sc Physics Quantum Mechanics-I - Question Paper
Degree
(For the Candidates admitted from 1993 arid awards) M.Sc. DEGREE IXAMWAflOM, APRIL 2000. Second Semester Part III Physics QUANTUM MECHANICS ~ I Time Three hours Maximum : 100 marks
Answer ALL questions.
SECTION A (10 x 2 = 20 marks)
1 If \P) ~ jA)+|S) then {P\ is
(a) |A)+{B| ! (A|+(B|
2 By variation method
(c) ' jv*&vd% <o
(d) j.ye*HyfdB >E
u. i'or this adiabatic approximation, the condition
that implies, ;,Cw(rt2j~probability of findir-*
the system at a* in a tinst sec).
W V%"1
km2 oi .
8*
(c)
(d)
JziJ.i0Jm} value is
(a) mkJ}m '
(b) (m -l)hJj/jn
(c) im + Dhp'lmt
The matrix for Z-eomponent of Dirac matrix c
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(a) (A |
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8, If A be a self adjoint operator, what is the value of {$ jilr)?
A
7, Write down the Hamiltonian for He atom.
8. What is .he percentage value of subsidiary peaks of main curve for the transition probability curves
. J'
L\b
drawn between 4 sin
y -Jn vernj afi?
9. Write down the matrix for Lt.
10. What is the magnetic moment for Dirac electron?
Answer ALL questions,
11, (a) Give any four properties of lira and het vectors. .
Or
Cb) Explain Hillberts space,
12, (a) Give the. theory of time indpendant perturbation theory for non-degenerate case: Briefly
explain the principle.
Or
(b) Discuss variation method to obtain the most suitable trial wave function for the system.
13. (a) Apply time dependent perturbation theory for the cast of inelastic collision.
Or
(b) Explain suddeiTdpproximati.on. Bring out the differences between adiabatic and sudden
approximations,
14. (a) Show that [J2, JJ * 0.
Or
(b) Show that fj,, J+.] k Jt where
j * = j j. jt y
15. (a) Derive Klein Gordon equation.
Or
<b) State the properties of gamma matrices, (any
four).
SECTION C (5 x8 = 40 marks)
Answer ALL the questions.
16, (a) Discuss the problem of harmonic oscillator by matrix mechanics method.
Or
(b> For the periodic potential, sing Kxonig-Penny model, obtain the necessary solutions.
17 {a) Discuss first order time independent perturbation theory for degenerate stationary state. Obtain corrected eigea function and eigen value.
Or
(b) ''Describe stark effect in Hydrogen. Derive expression for the energy separation A between lines, in the spectrum.
IS. (a) Derive expression for the transition probability between states for harmonic perturbation.
, Or
(b) Discuss, the problem of scattering of a particle by a potential.
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19. (a) Obtain eigen values for J * and Jt. '
Or
Cb) Obtain matrices for Lx,LytLz in terms of Pauls spin matrices,
20. (a) Develop Dirac's equation (relativistic) for a free particle and obtain plane wave solution,
. Or :
*
Cb) Discuss neve energy states. - y
SECTION D ~ (2 x 10 * 2 marks) ' ]
21. (a) Give the complete theory of WKB approximation for a particle placed in a slowly varying potential.
Or
(b) Calculate the transition probability coefficient
sB for adiabatic approximation.
22. (a) bain Clebsb-Gordan coefficients for . 1 . v 1 1 , J-
h - J% = mrs 2 = 2*
(b) Show that the energy E calculated by Dirac for Hydrogen atom is less than that done by
Schrodinger and the 3 calculated using Diracs
, , , r2io02Cm-~ 1) , Z
concept m given by--wirra r = 7-.
n zn **
6 4521
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Attachment: |
| Earning: Approval pending. |
