MSc Third Semester Physics Previous Year Question Papers | Msc Physics Quantum Mechanics Question Paper 2025
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B010902T
M.Sc. (Third Semester) ODD Semester
(NEP) Examination, 2024-25
PHYSICS
(Quantum Mechanics-II)
Time: Two Hours ] [Maximum Marks: 75
Section-A
(Short Answer Type Questions)
Note: Attempt all questions.
1. (a) A simple harmonic oscillator of mass ‘m’ and angular frequency ‘w’ is perturbed by an additional potential ‘bx3’, where ‘b’ is a parameter independent of x. Evaluate first order correction to the ground state energy of the oscillator.
Give ground state wave function
(b) Explain the variational method of finding the energy of the ground state of a system.
(c) Using the quantization rule for the phase integral, obtain the energy levels of a linear harmonic oscillator.
(d) A system in an unperturbed state ‘n’ is suddenly subjected to a constant perturbation ‘H’ (r)’ which exists during time 0-t. Find the probability for transition from state ‘n’ to state ‘k’.
(e) Calculate the electric dipole transition moment <2py |uz | 2s> for the 2s–2p, transition in a hydrogen atom.
(f) What is scattering amplitude? How is it related to scattering cross-section?
(g) Discus the validity conditions for Born approximation.
(h) Show that the Dirac matrices ax, ay, az and ẞ anticommute in pairs and their B squares are unity.
(i) White Dirac’s equation for a free particle. Find the form of the position probability density and the probability current density in Dirac’s formalism.
MSC Physics previous year Question Paper
Section-B
(Long Answer Type Questions)
Note: Attempt any one question.
2. Outline the perturbation theory applicable for the stationary state problems and
deduce expression for the first order and second order perturbation corrections when the energy levels of the unperturbed state
are non-degenerate.
3. Using first-order degenerate perturbation theory, calculate the energy levels of the n=2 state of a hydrogen atom placed in an external uniform weak electric field along the positive z-axis. Draw an energy level diagram illustrating the different states in
the presence of the field:
Given: 200
4. What are adiabatic and sudden approximations in the time-dependent perturbation theory and under what conditions they are valid?
5. Deduce the transition probability per second for spontaneous emission of radiation under dipole approximation.
M.Sc 3rd Semester Physics (Quantum Mechanics-II) Question Paper 2025
Section-C
(Long Answer Type Questions)
Note: Attempt any one question.
6. Derive an expression for the scattering amplitude in the Born approximation. Using the born approximation method, calculate the differential cross-section for the scattering by a square well potential
defined by: v(r)=-v0 r<b
=0 r>b
7. Obtain an expression for differential scattering cross-section and total cross- section using the method of partial wave analysis. State and prove the optical theorem.
8. Write down the Klein-Gordon equation. Show that this equation leads to positive and negative probability density values. How is this difficulty overcome?
9. Obtain the plane-wave solutions of the Dirac equation. What is a hole?
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