M.Sc. DEGREE EXAMINATION, APRIL 2016
Physics
QUANTUM MECHANICS II
(2011 onwards)
Time 3 Hours Maximum 75 Marks
Part A (10 2 20)
Answer all the questions.
1. Define angular momentum and write its uncertainty
relation.
2. Write down the Pauli spin matrices.
3. Are the wave functions of bosons symmetric? Why?
4. What are the uses of Dirac's bra and ket vectors?
5. What is self-consistent field approximation?
6. What is the advantage of Hartree-Fock method over
Hartree method?
7. What is the relativistic equation used for treating
spin-1/2 particles?
8. What is known as antimatter?
9. Define the particle density operator in Fock space.
10. Write the relation between Hamiltonian density and total
Hamiltonian.
Sub. Code
521302
RW-10946
2
hp-ap1
Part B 5 25)
Answer all the questions, choosing either or
11. Evaluate the commutator L being the
angular momentum operator.
Or
Derive Pauli's spin matrices.
12. Show that the permutation operator is hermitian.
Or
Discuss the interaction picture of representing
dynamical variables.
13. Explain the Hartree method of solving a many-body
problem.
Or
Explain the use of quantum mechanical electronic
structure of atoms in the design of modern periodic
table of elements.
14. Derive Dirac Hamiltonian.
Or
For the Dirac -matrices, show that 0 for
I .
15. Derive an expression for the canonical momentum
by using the Lagrangian density.
Or
Explain the ground state properties of a field with N
spinless fermions.
RW-10946
3
hp-ap1
Part C 10 30)
Answer any three questions.
16. Discuss the theory of addition of two angular momenta
and obtain the CG coefficients for j 2 system.
17. Solve the harmonic oscillator by using the matrix
representation method.
18. Explain in detail the Thomas-Fermi model of atoms.
19. Solve the Klein-Gordon equation for free particles and
explain the important characteristics of the energy
spectrum.
20. Discuss the theory of quantizing the normal modes of EM
field.