PH 2806 / 2801 – QUANTUM MECHANICS – I

Date : 03/05/2008 Dept. No. Max. : 100 Marks

Time : 1:00 – 4:00

PART A ( 10 X 2 = 20 MARKS )

ANSWER ALL QUESTIONS. EACH QUESTION CARRIES 2 MARKS.

What is meant by classical approximation in wave mechanics ?
Can classical concepts explain the Compton effect ?
Define probability density and probability current density.
What are stationary states ?
What is an observable ? Give an example.
State the expansion postulate.
Sketch the first two wave functions of the stationary states of a simple harmonic oscillator.
What are coherent states ?
What is the effect of an electric field on the energy levels of an atom ?
What is the origin of the exchange interaction ?

PART B ( 4 X 7.5 = 30 MARKS )

ANSWER ANY FOUR QUESTIONS. EACH QUESTION CARRIES 7.5 MARKS.

State and explain the uncertainity principle.
(a) Explain Born’s interpretation of the wave function.

(b) Explain the significance of the equation of continuity.

(a) Explain the principle of superposition.

(b) Explain the property of closure.

Solve the eigenvalue equation for L² by the method of separation of variables.
Explain the use of perturbation theory for the case of a 2-d harmonic oscillator.

PART C ( 4 X 12.5 = 50 MARKS )

ANSWER ANY FOUR QUESTIONS. EACH QUESTION CARRIES 12.5 MARKS.

Describe Compton effect and derive an expression for the shift in wavelength of the scattered beam.

17.Consider a square potential barrier on which is incident a beam of particles of energy E. Calculate the reflected intensity and transmitted intensity, if the barrier height is V and width is a.

(a) Discuss the eigenvalue problem for the momentum operator.

(b) Discuss the postulate regarding evolution of a system with time.

Obtain the Schrodinger equation for a linear harmonic oscillator and find its eigenvalues and

eigenfunctions.

Discuss the WKB approximation method of solving eigenvalue problems. Consider the 1-d case and

find the solution near a turning point.

Go To Main page