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Madras University Msc Physics Exam Question Paper |

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Re: Madras University Msc Physics Exam Question Paper
Here I am providing few questions of the Madras University Msc Physics Exam Question Paper which you are looking for . 1. Only Hermitian operators are associated with physical quantities. Why? 2. What is box normalization? 3. Define the ladder operators of harmonic oscillator. 4. What is degeneracy? Give an example. 5. Write down the operators for position and momentum in coordinate representation. 6. Explain symmetric and antisymmetric wave functions with examples. 7. Why the hydrogen atom in the ground state does not show a first-order Stark effect? 8. The result of the variation method always gives an upper limit for the ground state energy of the system. Why? 9. What are spinors? Verify that they form a complete set of basis. 10. Find the orbital angular momenta of two electrons, (a) both in p-orbitals, (b) in the configuration p1d1. PART B — (5 6 = 30 marks) Answer ALL questions. All questions carry equal marks. 11. (a) Obtain the time-dependent Schr o& & dinger's equation and separate it into space and timedependent parts. Or (b) Show that the eigenvalues of a Hermitian operator are real and the eigenfunctions of a Hermitian operator belonging to different eigenvalues are orthogonal. 12. (a) Write the Hamiltonian for hydrogen atom and reduce the two-body hydrogen problem into one-body problem. Or (b) Solve the radial part of Schr o& & dinger equation for hydrogen atom and obtain its energy eigenvalues. 13. (a) Explain space inversion symmetry. Or (b) Distinguish between the Heisenberg and Schr o& & dinger pictures. P/ID 40003/PPHC 3 14. (a) State and prove the upper bound theorem of the variation method. Or (b) Workout the splitting of the S P 1 1 transition of an atom placed in a magnetic field B along z-axis. 15. (a) For Pauli's matrices, prove that : (i) y x , z i 2 , (ii) . i z y x Or (b) Obtain the matrix representation of J2 and Jx for j = 1. PART C — (5 10 = 50 marks) Answer ALL questions. All questions carry equal marks. 16. (a) State and describe the Ehrenfest's theorems. Or (b) State Uncertainly principle. Establish the fact of non-existence of free electrons in the nucleus using uncertainty principle. 17. (a) Derive the transmission coefficient. T and the reflection coefficient, R of a stream of particles of mass m and energy E moves towards the potential step of height V0 < E and show that (b) Obtain the energy eigenvalues and normalized energy eigenfunctions of a particle in the 1D infinite potential well. 18. (a) Derive the equations of motion for states and operators in the Heisenberg and interaction pictures. Or (b) Show that the total angular momentum of a particle with spin is the generators of the infinitesimal rotation. 19. (a) Calculate the first-Order Stark effect of the level n = 2 of the hydrogen atom. Or (b) Discuss the WKB approximation method to a case in which the potential energy is a slowly varying function of position. 20. (a) Discuss the first-order time-independent perturbation theory for non-degenerate stationary state. Obtain the corrected eigen functions and eigenvalue. Or (b) Obtain the Clebsh-Gordan coefficients for a system having j1 = 1 and j2 = 1/2. |