Quantum Mechanics Important Questions

Bsc/Msc Physics 

Unit 1: Approximation Method for Bound States 

1. Explain Perturbed Harmonic oscillator?
2. Explain degenerate and non degenerate levels?
3. What is the Variation method (Rayleigh—Ritz method)? Find out the ground state energy of Helium atom with it?
4. Explain W.K.B. Approximation method?
5. Explain Time independent perturbation theory?
6. Explain the physical applications of non degenerate perturbation theory — 1. The Perturbed Harmonic oscillator, 2. Two electron system (Normal Helium Atom)?
7. Explain the theory of α/alpha decay by the W.K.B. Approximation?
8. Using Variation method evaluate energy eigen values of normal state of hydrogen atom?
9. What is the Stark effect? Explain the stark effect in the hydrogen atom?

Unit 2: Time dependant perturbation theory 

1. Explain method of variation of constants and transition Probability?
2. Explain the adiabatic approximation method?
3. Explain the sudden approximation method?
4. Derive the wave equation for a system of charged particles under the influence of external electromagnetic field?
5. Explain Time dependent perturbation theory?
6. Explain the Fermi—golden rule/Transition Probability?
7. Explain the harmonic perturbation?
8. Explain the motion of charged particles in a electromagnetic field?
9. Explain Einstein's A and B coefficients?
10. Derive expression for Einstein's transition Probability by perturbation theory?
11. Explain absorption and induced emission of charged particles?

Unit 3: Scattering 

1. Explain The theory of scattering?
2. Define scattering amplitude and scattering cross section?
3. Find the differential scattering cross section with the help of particle wave analysis?
4. Explain Born approximation? Derive the condition for validity of it?
5. Derive Born approximation theory for  scattered wave with weak interaction?
6. Write the conditions for the validity of the Born approximation?
7. What is particle wave analysis in quantum mechanics?
8. Define spherically symmetric potential and identical particles with spin?
9. Explain pauli's spin matrices?
10. Explain the scattering by perfectly rigid sphere?

Unit 4: Schrodinger's Relativistic equations 

1. What is the K.G. equation? Derive the equation of continuity from the K.G. equation?
2. Derive K.G. equation in electromagnetic field?
3. Derive Dirac's equations for free particle?
4. Explain Dirac's relativistic equation in electromagnetic field?
5. What is Dirac's equation?
6. What is hyperfine splitting?
7. Explain dirac's matrices?
8. Derive K.G. equation for hydrogen atom?
9. Derive dirac's relativistic equation for free electron?
10. Explain probability and current density by K.G. equation?
11. Write detailed notes on the following — 1. Negative energy state and their interpretation hydrogen atom 2. Relation between angles in L system and C system?