M.Sc. DEGREE EXAMINATION, NOVEMBER 2017
Third Semester
Physics
QUANTUM MECHANICS
(CBCS 2014 onwards)
Time 3 Hours Maximum 75 Marks
Part A (10 x 2 20)
Answer all questions.
1. Define the inner products in terms of Dirac's Bra and Ket
vector notation.
4. Write down the energy eigen values and eigen functions
of a rigid rotator.
2. State the advantage of the method of variation of
constants.
3. Write down the ground state wave function 0 of
hydrogen atom.
Sub. Code
4MPH3C1
AFF-4869
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Wk 6
4. Define a partile exchange operator.
5. What is the principle of partial wave analysis?
6. What are the properties of position?
7. Write down the four Dirac's matrices.
Part B x 5 25)
Answer all questions.
11. Explain expectation valves for various operators.
Give a physical interpretation of the wave function.
Or
State and prove Heisenberg's uncertainty principle.
12. Solve the radial part of the equation
for the hydrogen atom.
Or
Solve the problem of linear Harmonic oscillator
using Hermite's differential equation method.
13. Discuss the first order time independent
perturbation theory for non-degenerate case.
Or
Explain about sudden approximation.
14. Evaluate the C.G. Coefficients for
2
1
j1 j2 .
Or
Discuss Born's approximation and state the
conditions for validity criterion of this
approximation.
AFF-4869
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Wk 6
15. For a particle which is moving in a central force
field potential, shown that the orbital angular
momentum is not a constant of motion.
Or
Obtain an expression for the magnetic moment of
an electron.
Part C 10 30)
Answer any three questions.
16. Solve Schroedinger's wave equation for a particle in a
square well potential and get the energy eigen valves and
eigen functions.
17. Solve the wave equation for a rectangular
potential barrier and find expressions for reflection and
transmission coefficients. Show their sum is unity.
18. Discuss in detail the time dependent perturbation theory
and obtain Fermi's Golden rule.
19. Discuss general formulation of scattering theory and
using Green's function find expressions for scattering
amplitude and scattering cross section.
20. Using Dirac's electron theory obtain a relation between
spin and magnetic moment of electron.
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