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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034 B.Sc. DEGREE EXAMINATION – PHYSICS SIXTH SEMESTER – APRIL 2008 PH 6603 - QUANTUM MECHANICS & RELATIVITY Date : 28-06-08 Time : 9.00 – 12.00 Dept. No. Max. : 100 Marks PART – A Answer ALL questions. (10 x 2 = 20) 1. What is meant by matter waves? 2. State Heisenberg uncertainty relation. 3. What do you mean by eigen values and eigen functions 4. State Ehrenfest theorem. 5. Write down any two postulates of wave mechanics. 6. What is a Hermitian operator? 7. Distinguish inertial and non-inertial frames of reference? 8. If 5Kg of a substance is fully converted into energy, how much energy is produced? 9. State the postulates of general theory of relativity. 10. What is gravitational red shift? PART – B Answer any FOUR questions. (4 x 7.5 = 30) 11. a) Check the validity of Heisenberg’s uncertainty principle in the diffraction of an electron beam by a single slit? (5) b) Calculate the de-broglie wavelength of an particle which has bean accelerated through a p.d of 2000 v. (2.5) 12. Starting from time-dependent form of Schrödinger’s equation, obtain the time independent form. 13. Evaluate i) [x, Px] and [Lx, x]. (4 + 3.5) 14. Deduce the expression for the law of addition of velocities. 15. Explain the Principle of equivalence. PART – C Answer any FOUR questions. (4 x 12.5 = 50) 16. a) Describe Davission and Germer experiment for the study of electron diffraction (9) b) Discuss the results of the experiment. (3.5) 17. a) Establish Schrodinger’s equation for a linear harmonic oscillator. (9) b) Obtain its eigen values and eigen functions. (3.5) 18. a) Formulate Schrodinger’s equation for a rigid rotator. (10) b) Find its eign values and eigen functions. (2.5) 19. Deduce the formula for the relativistic variation of mass with velocity. Explain its significance. 20. Discuss the following experimental observations of general relativity. a) gravitational red shift b) planetary motion and c) bending of light.(4.5+4+4) ************* 1