LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – PHYSICS

XC 23

SIXTH SEMESTER – April 2009

PH 6605 – QUANTUM MECHANICS & RELATIVITY

 

 

 

Date & Time: 18/04/2009 / 9:00 – 12:00      Dept.                                                         : 100 Marks

 

 

SECTION – A

 

Answer all the questions.                                                                                            (10×2 = 20 Marks)

1. State Heisenberg’s uncertainty principle. Give a mathematical form of the principle.
2. What is Compton effect?
3. Define probability current density.
4. What is tunnel effect?
5. Show that [ L_x, L_y ] = iħL_z.
6. Express the operator for angular momentum component L_x in spherical polar coordinates.
7. What are inertial and non – inertial frames of references?
8. At what speed is a particle moving if the mass is equal to three times its rest mass?
9. What is Mach’s principle?
10. State the postulates of General theory of relativity.

SECTION – B

Answer any four questions.                                                                                      (4×7.5 = 30 Marks)

11. (a) What is the principle of an electron microscope?                                                       (2)

(b)        Describe the working of an electron microscope with a diagram.                        (4+1.5)

12. Solve the Schrödinger equation for the linear harmonic oscillator and obtain its energy levels.                                                                                                                   (5.5+2)
13. (a) What is a Hermitian operator?                                                                                 (2.5)
    • Show that the eigen values of Hermitian operators are real. (5)
14. (a) Derive Einstein’s mass – energy relation.                                                                (5.5)
    • Explain mass – energy equivalence with two examples. (2)
15. Discuss planetary motion on the basis of Einstein’s theory of gravitation and interpret the path of the planet about the sun.           (7.5)

 

 

SECTION-C

Answer any four questions.                                                                           (4×12.5 = 50 Marks)

16. (a) What are matter waves? (2)

(b) Describe Davisson – Germer experiment to confirm the concept of matter waves.          (10.5)

17. Starting from the time dependent Schrodinger equation, obtain the time independent

Schrodinger equation.                                                                                                      (6.5+6)

18. Write down the radial part of the time-independent Schrödinger wave equation for the hydrogen atom and solve the equation to obtain the Eigen values of the energy of the atom. (10+2.5)
19. (a) Describe Michelson – Morley experiment and explain the physical significance of the

negative result.                                                                                                             (8+2.5)

(b) How fast would a rocket have to go relative to an observer for its length to be contracted

to 99% of its length at rest?                                                                                                 (2)

20. (a) Derive an expression for gravitational red shift. (6.5)

(b) Write a note on bending of light rays in a gravitational field.                                                (6)

 

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