Quantum Mechanics - Ii

Course: M.Sc Code: GH-552 Branch: Physics Year: 2022

Download Original PDF

Get the official Barkatullah University print version scanned document.

Download/Print

🤝 Help Your Juniors!

Have previous year question papers that aren't on our website? Help the next batch of students by sending them to us! With your consent, we will proudly feature your name as a Top Contributor on our platform.

Submit Papers 📩
Roll No. ........................
Total No. of Questions : 11
Total No. of Printed Pages : 7
GH-552
M.Sc. IInd Semester (Reg./ATKT)
Examination, 2022
Physics
Paper - I
Quantum Mechanics - II
Time : 3 Hours
[Maximum Marks : 85
Note : - Attempt all questions. Each questions carry equal marks.
SECTION - 'A'
5x3=15
Objective Type Questions
1.
Choose the correct answer.
(i)
Which one of the following is correct.
  1. The zero point energy of harmonic oscillator is 3/2ℏωc
  2. The adiabatic approximation the perturbation inturned on very fast
  3. For low energy particular the gross-section is four times the geometrical cross-section of rigid sphere
  4. Accroding to the dirac theory orbital angular momentum, L commutes with H.
(ii)
Equation of continuity is
  1. ∇.s(r,t) + ∂ρ/∂t = 0
  2. ∇.s(r,t) - ∂ρ/∂t = 0
  3. ∇2.s(r,t) + ∂ρ/∂t = 0
  4. ∇.s(r,t) + ∂ρ/∂p = 0
(iii)
The criterion of the validity of born-approximation is
  1. The incident wave should be much smaller as compared to the scattered wave
  2. The incident wave should be much larger as compared to the scattered wave
  3. The Scattered wave should be much larger as compared to the incident wave
  4. The Scattered wave should be much smaller as compared to the incident wave
(iv)
Which one of the following is a paulis' spin matrices associated with the component of spin angular momen-tum Sx = 1/2ℏ
  1. σx = [[0, 1], [1, 0]]
  2. σx = [[0, 1], [1, 0]]
  3. σx = [[1, 0], [0, -1]]
  4. σx = [[0, -i], [i, 0]]
(v)
The splitting of energy levels of an atom caused by a uniform external electric field E is called as:
  1. Zeeman effect
  2. Stack effect
  3. Hall effect
  4. Raman effect
SECTION - 'B'
5x5=25
Short Answer Type Questions
2.
Describe W.K.B method.
OR
Explain the first order stock effect in Hydrogen atom.
3.
Discuss the method of variation of constant and transition prob-ability.
OR
Explain the adiabatic approximation.
4.
Describe paulis spin matrices.
OR
Explain Born-approximation.
5.
Obtain Dirac relativistic equation for free electron.
OR
Prove that
∂2ψ/∂t2 = (-ℏ2c2∇2 + m2c4)ψ
6.
Write notes on any two of the following :-
  1. connection formulae.
  2. Einstein A and B' coefficient.
  3. Distinguishability of identical particles.
  4. Hyperfine splitting.
SECTION - 'C'
9x5=45
Long Answer Type Questions
7.
State and prove the variation principle for obtaining approxi-mate energies. Use it to find the ground state of energy of Helium.
OR
Explain Rayleigh-Schrodinger perturbation theory of degenrate case.
8.
Give the theory of induced emission and absorption of radia-tion on the basis of time dependent perturbation theory.
OR
Obtain the wave equation for a system of charged particles under the influence of external electromagnetic field.
9.
Explain why the method of partial waves is suitable for the scattering of slow particles by the spherically symmetric field. Derive an expression for differential scattering cross section in terms of phase shift.
OR

fk(θ) represents the scattering amplitude in the asymptotic wave function.

Ψ(A) = eikr + fk(θ)/r e-ikr

Prove that the differential crossection.

σ(θ) = |fk(θ)|2
10.
Obtain the Klein-Gordan equation in presence of electromag-netic field.
OR
Verify that the probability density and current density defined for dirac equation satisfy the continuity equation.
11.
Write short notes on any two of the following :-
  1. Perturbation theory of non-degenerate case
  2. Scattering by a perfectly rigid sphere
  3. Sudden approximation
  4. Dirac relativistic equation in electromagnetic field.
GH-552
(7)
Copies 1000