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ROLL NO. ....................
SECTION - 'A'
Short Answer Type Questions
MN-514
M.Sc. 1st Semester (Reg./ATKT)
Examination, 2023-24
Physics
Paper - III
Quantum Mechanics - I
Time : 3 Hours
[Maximum Marks : 85]
Note : There are two section A & B. Section A is short answer questions each carry 7 mark part B long answer each carries 10 mark.
1.
What is Linear Harmonic Oscillator?
OR
Explain Pauli's exclusion principle?
Explain Pauli's exclusion principle?
2.
Explain Hilbert space ?
OR
How we define creation, annihilation and number operators?
How we define creation, annihilation and number operators?
3.
What is Zeeman Effect without electron spin?
OR
Derive an expression for transistion probability?
Derive an expression for transistion probability?
4.
Explain concept of spin?
OR
What do you understand by adiabatic and sudden approximation?
What do you understand by adiabatic and sudden approximation?
5.
Explain Heisenberg and interaction pictures?
OR
Derive the commutation relation of J2 with Jx and Jy, where J+ = Jx + iJy and J- = Jx - iJy
(a) [J2, Jx]
(b) [J2, Jy]
Where J2 = Jx2 + Jy2 + Jz2
Derive the commutation relation of J2 with Jx and Jy, where J+ = Jx + iJy and J- = Jx - iJy
(a) [J2, Jx]
(b) [J2, Jy]
Where J2 = Jx2 + Jy2 + Jz2
OR
Derive an expression for time dependent perturbation theory.
Derive an expression for time dependent perturbation theory.
4.
Give the theory of first order Stark effect on the basis of quantum mechanics.
OR
Discuss the first order perturbation theory for a non-degenerate level.
Discuss the first order perturbation theory for a non-degenerate level.
5.
State and explain Fermi's golden rule.
OR
Derive the expression for Clebsch-Gordan coefficient ?
Derive the expression for Clebsch-Gordan coefficient ?
SECTION - 'B'
Long Answer Type Questions
1.
Obtain the Schrödinger's equation for spherically symmetric potentials in three dimensions ?
OR
Establish Schrödinger's equation for a linear harmonic oscillator ?
Establish Schrödinger's equation for a linear harmonic oscillator ?
2.
Obtain Pauli's spin matrices and illustrate their properties ?
OR
Discuss Stern-Gerlach Experiment ?
Discuss Stern-Gerlach Experiment ?
3.
Describe W.K.B. method for the solution of Schrodinger wave equation in a potential field and discuss its validity ?