Loyola College M.Sc. Physics Nov 2003 Quantum Mechanics II Question Paper PDF Download

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

M. Sc., DEGREE EXAMINATION – PHYSICS

THIRD SEMESTER – NOVEMBER 2003

PH 3800 / PH 920 – QUANTUM MECHANICS II

 

03.11.2003                                                                                           Max.   : 100 Marks

1.00 – 4.00

SECTION – A

 

Answer ALL the questions.                                                                         (10 x 2 = 20)

 

  1. If the eigen values of A are ‘a’, then show that where  is the projection operator.
  2. Prove that e-i a Px / is unitary when a is a real parameter.
  3. Evaluate <jm | J – J + | jm>
  4. Show that e
  5. What is first Born approximation?
  6. State optical theorem.
  7. Explain dipole approximation.
  8. What are allowed and Forbidden transitions with respect to the selection rules of the dipole approximation.
  9. Mention the disadvantage of Klein – Gordan equation for relativistic particles.
  10. What is the significance of the negative energy state?

 

SECTION – B

 

Answer any FOUR questions.                                                                                (4 x 7.5 = 30)

 

  1. Show that has the form – i in the Schroedinger representation.
  2. Obtain the G.  Coefficients  for  the  coupling  of  two  spin  angular  momenta  (j1 = j2 = ½).
  3. Arrive at an expression for the scattering amplitude using Green’s functions.
  4. Explain the Schroedinger picture of time evolution.
  5. Obtain the explicit form for matrices in the Dirac Hamiltonian.

 

SECTION – C

 

Answer any FOUR questions.                                                                              (4 x 12.5 = 50)

 

  1. Arrive at an expression for a proper choice of basis set for commuting operators.
  2. Obtain the  matrix  representation for  J2, Jx,  Jy, Jz  in the |jm> basis for j = 1 and j = 3/2.
  3. Explain the partial wave analysis and derive an expression for the scattering amplitude in terms of phase shifts.
  4. Derive an expression for transition probability of upward and downward transition for an atom interacting with an electromagnetic radiation.
  5. Determine the eigenvalues and eigenfunctions of a free particle using Dirac’s Haneiltonian.

 

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