Quantum Mechanics-Ii

(i) α-particle consists of :

1. 2p⁺ and 2n⁰ only
2. 2e, 2p⁺ and 2n⁰
3. 2e and 4p only
4. 2p only

(ii) The particle of mass m is trapped in an infinite quantum well of width L. The expectation value of its momentum in the third excited state is :

1. Infinity
2. πL
3. Zero
4. 

(iii) The Schrödinger wave equation is :

1. Quadratic
2. Linear
3. Differential
4. Derivable

(iv) Einstein's A and B coefficient are proportional to :

1. the cube of frequency
2. the square of frequency
3. the voltage
4. None of the above

(v) An electron in ground state of a H-atom. The probability that it is within the Bohr radius is approximately equal to :

1. 0.32
2. 0.60
3. 0.16
4. 0.90

2. Describe in brief theory of α-decay.

Or

What is perturbation theory ? What are its applications ?

3. What do you understand by Einstein's A and B coefficients ?

Or

What is transition probability ?

4. Describe in brief theory of scattering.

8. Explain with the help of methods of variation the adiabatic and sudden approximation.

Or

Derive wave equation for a system of charged particles under the influence of external electromagnetic field.

9. Explain Born approximation and partial waves in detail.

Or

Derive expression of scattering by perfectly rigid sphere.

10. Explain Klein-Gordon equation in presence of electromagnetic field. Apply it for a hydrogen atom.

Or

With the help of Dirac's relativistic equation, explain negative energy states and its application to hydrogen atom.

(a) Theory of α-decay on the basis of potential barrier

(b) Absorption and induced emission

(c) Identical particles with spin

(d) Hyperfine splitting.