LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

XC 21

B.Sc. DEGREE EXAMINATION – PHYSICS

SIXTH SEMESTER – April 2009

PH 6603 – QUANTUM MECHANICS & RELATIVITY

 

 

 

Date & Time: 18/04/2009 / 9:00 – 12:00          Dept. No.                                                    Max. : 100 Marks

 

 

                                                             PART – A

Answer ALL questions:                                                                                             (10×2=20 Marks)

 

1. What are the assumptions of Planck’s radiation law?
2. An electron is confined to a box of length 10^-10m.Calculate the minimum uncertainty in its

velocity.

3. What is a normalized wave function?
4. Express the potential function of a particle in a box of width ‘ ’ and of infinite height.
5. Explain the commutative property of operators with an example.
6. Write down the eigen value equation for L².
7. Show that acceleration is invariant in all inertial frames, according to classical relativity.
8. What is the velocity of π-mesons whose observed mean life is 2.5×10^-7s. The proper mean

life is  2.5×10^-8s.

9. What is principle of equivalence?
10. Explain the concept of gravitational lens.

PART – B

Answer any FOUR questions:                                                                          (4×7.5=30 Marks)

 

11. a) Explain de Broglie’s hypothesis of matter waves and derive an equation for the wavelength

of such waves.                                                                                                                         (4.5)

 

1. b) Calculate the de Broglie wavelength of waves associated with an electron which has been

accelerated from rest through a potential of 100V.                                                                   (3)

 

12. Calculate the energy levels of a particle in a one dimensional square well potential with

perfectly rigid walls.

 

13. Evaluate [x,P_x] and [L_x,L_y] (3.5+4)

 

14. a) Show that the length of an object appears to contract when moving with a velocity

comparable to that of light.                                                                                                     (5)

 

1. b) If the velocity of an object is 0.6c, find out the percentage of length contraction. (2.5)

 

15. Explain the basic ideas of general theory of relativity? Discuss the gravitational red shift

based on it.                                                                                                                              (3.5+4)

PART – C

Answer any FOUR questions:                                                                         (4×12.5=50 Marks)

 

16. a) Describe G.P.Thomson’s experiment to demonstrate the wave nature of electrons and

verify de Broglie’s hypothesis of matter waves.                                                                       (8)

 

 

4. b) Illustrate Heisenberg’s uncertainty principle with an example. (4.5)

 

17. a) Discuss the motion of a particle in a three dimensional box. Find the eigenvalues

and eigenfunctions.                                                                                                                   (9)

 

3. b) Explain non-degenerate and degenerate energy levels. (3.5)

 

18. Solve the Schrodinger’s equation for a hydrogen atom.

 

19. a) Derive the equations of Lorentz transformation. (10)

 

2. b) The total energy of a particle is exactly twice its rest energy. Calculate its speed. (2.5)

 

20. Discuss the following experimental observations which support general theory:

(i) Planetary motion and (ii) bending of light.                                                                        (6.5+6)

 

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