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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034 B.Sc. DEGREE EXAMINATION – PHYSICS SIXTH SEMESTER – SUPPLEMENTARY – JUNE 2012 PH 6609/PH 6605/6003/6600 - QUANTUM MECHANICS & RELATIVITY Date : 30-06-2012 Time : 2:00 - 5:00 Dept. No. Max. : 100 Marks PART A (10X 2 = 20) Answer ALL questions 1. Find the de Broglie wavelength associated with an electron moving with a speed 107m/s. 2. State Heisenberg’s uncertainty principle. 3. Write the Time independent Schrödinger’s equation. 4. Calculate the permitted energy levls of an electron in a box 1Åwide. 5. Show that [L+ ,L_] = 2 ћ Lz. 6. Calculate the magnitude of the orbital angular momentum of an electron with l = 3. 7. State the postutes of special theory of relativity. 8. The total energy of a particle is twice its rest energy. Calculate its speed. 9. What is length contraction? 10. State the principle of equivalence. PART B (4 x7. 5 = 30 ) Answer any FOUR questions. 11. Describe the experiment of G.P. Thomson on the diffraction of electrons... 12. Obtain the values of the energy of a particle in a one dimensional box. Indicate graphically the first three wave functions. 13. Set up and solve the schrodinger equation for a rigid rotator with free axis for its eigen values and eigen functions.. .. 14. Deduce an expression for the law of addition of relativistic velocities. The half life of a particle as measured in the laboratory , comes out to be 4 x 10 -8secondwhen its speed is 0.8c and 3 x 10-8 second when its speed is 0.6c. Show that this variation due to Time dilation. 15. Explain Gravitational red shift. PART C (4 x 12.5 = 50) Answer any FOUR questions 16. Describe Davisson – Germer’s experiment on the study of matter waves. 17. Establish Schrodinger’s equation for a linear harmonic oscillator and solve it to obtain its eigen values and eigen functions. 18. (a)Write the operators corresponding to the various rectangular components of angular momentum in spherical polar coordinates. (2.5) (b) Deduce an expression for the operator of the square of angular momentum is spherical polar coordinates. (10) 19. (a)Explain variation of mass with velocity. (b)Calculate the K.E. of an electron moving with velocity of 0.98c in the laboratory system. (10) (2.5) 20. (a) Discuss particle wave duality. (b)Explain bending of light rays in a gravitational field. (5) (7.5) $$$$$$$