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20th August 2014, 11:26 AM
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Join Date: Apr 2013
Re: Madras University Msc Physics Exam Question Paper

Here I am providing few questions of the Madras University Msc Physics Exam Question Paper which you are looking for .

1. Only Hermitian operators are associated with
physical quantities. Why?
2. What is box normalization?
3. Define the ladder operators of harmonic oscillator.
4. What is degeneracy? Give an example.
5. Write down the operators for position and
momentum in coordinate representation.
6. Explain symmetric and antisymmetric wave
functions with examples.
7. Why the hydrogen atom in the ground state does
not show a first-order Stark effect?
8. The result of the variation method always gives an
upper limit for the ground state energy of the
system. Why?
9. What are spinors? Verify that they form a
complete set of basis.
10. Find the orbital angular momenta of two
electrons,
(a) both in p-orbitals,
(b) in the configuration p1d1.

PART B — (5 6 = 30 marks)
Answer ALL questions.
All questions carry equal marks.
11. (a) Obtain the time-dependent Schr o& & dinger's
equation and separate it into space and timedependent
parts.
Or
(b) Show that the eigenvalues of a Hermitian
operator are real and the eigenfunctions of a
Hermitian operator belonging to different
eigenvalues are orthogonal.
12. (a) Write the Hamiltonian for hydrogen atom and
reduce the two-body hydrogen problem into
one-body problem.
Or
(b) Solve the radial part of Schr o& & dinger equation
for hydrogen atom and obtain its energy
eigenvalues.
13. (a) Explain space inversion symmetry.
Or
(b) Distinguish between the Heisenberg and
Schr o& & dinger pictures.
P/ID 40003/PPHC 3
14. (a) State and prove the upper bound theorem of
the variation method.
Or
(b) Workout the splitting of the
S P 1 1 transition of an atom placed in a
magnetic field B along z-axis.
15. (a) For Pauli's matrices, prove that :
(i)   y x , z i 2 ,
(ii) . i z y x 
Or
(b) Obtain the matrix representation of J2 and Jx
for j = 1.
PART C — (5 10 = 50 marks)
Answer ALL questions.
All questions carry equal marks.
16. (a) State and describe the Ehrenfest's theorems.
Or
(b) State Uncertainly principle. Establish the fact
of non-existence of free electrons in the
nucleus using uncertainty principle.
17. (a) Derive the transmission coefficient. T and the
reflection coefficient, R of a stream of particles
of mass m and energy E moves towards the
potential step of height V0 < E and show that

(b) Obtain the energy eigenvalues and
normalized energy eigenfunctions of a particle
in the 1D infinite potential well.
18. (a) Derive the equations of motion for states and
operators in the Heisenberg and interaction
pictures.
Or
(b) Show that the total angular momentum of a
particle with spin is the generators of the
infinitesimal rotation.
19. (a) Calculate the first-Order Stark effect of the
level n = 2 of the hydrogen atom.
Or
(b) Discuss the WKB approximation method to a
case in which the potential energy is a slowly
varying function of position.
20. (a) Discuss the first-order time-independent
perturbation theory for non-degenerate
stationary state. Obtain the corrected eigen
functions and eigenvalue.
Or
(b) Obtain the Clebsh-Gordan coefficients for a
system having j1 = 1 and j2 = 1/2.


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