(DPHY 01) M.Sc. DEGREE EXAMINATION, DECEMBER 011. First Year Physics Paper I MATHEMATICAL PHYSICS Time : Three hours Maximum : 100 marks Answer any FIVE questions. All questions carry equal marks. 1. (a) Starting from the Legendre s differential equation, prove the orthonormal property. Evaluate Jy ( ) and 1 ( x), hence show that J s / ( x) x J sinx cosx. x x. (a) Using Hermite polynomial prove that e x H ( x) H n m ( x) dx n n! n nm Prove that recurrence relation of Hermite 1 polynomial Hn( x) nhn1( x), ( n 1) where 1 H ( x) 0. 0.
3. (a) State and prove cauchy s integral formula. sinz cosz Evaluate dz, z 3. ( z 1)( z ) c 4. (a) State and prove Laurent s theorem. Find the residue of z/ z 1 z 4 z. 5. (a) Mention the different types of tensors. Give the transformation laws of tensor s of 3rd order. Distinguish between contra variant and covariant tensors. 6. (a) State and prove quotient law of tensor. Explain the terms symmetric and antisymmetric tensors. 7. (a) State and prove Laplace transform of derivatives. Evaluate 1 6 34s 86s L. s3 9s 16 16s 9 8. (a) Find the Fourier cosine and sine integrals of Fourier series. Find the solution for the triangular wave using Fourier series. (DPHY 01)
9. Answer any TWO of the following : 1 1 l ( l1 l1 (a) Prove that P x) xp ( x) lp ( x). (c) (d) State and explain Morera s theorem. Show that Kronecker delta function is a mixed tensor of rank two. State and prove First-and second shifting property of Laplace transform. 3 (DPHY 01)
(DPHY 0) M.Sc. DEGREE EXAMINATION, DECEMBER 011. First Year Physics Paper II CLASSICAL MECHANICS AND STATISTICAL MECHANICS Time : Three hours Maximum : 100 marks Answer any FIVE questions. All questions carry equal marks. 1. (a) State and explain the principle of Virtual work. From D Alembert s principle deduce the Lagrangian equation of motion.. (a) Explain the principle of Least action. Describe Corialis force with suitable example. 3. (a) State and explain the fundamental postulate of special theory of relativity and obtain Lorentz transformations using these postulates. Obtain Hamilton-Jacobi equation for Hamilton s principle function.
4. (a) What are molecular vibrations? Explain. Discuss free vibration of a linear triatomic molecule. 5. (a) Explain the postulates of classical mechanics. Distinguish between micro canonical, canonical and grand canonical ensembles. Discuss the equi partition theorem. 6. (a) Give a role of Gibb s paradox. Explain density fluctuations in the grand canonical ensemble. 7. (a) Explain the foundation of statistical mechanics. Explain the classical limit of the partition function. 8. (a) State and explain the variational principle. Obtain the relation between pressure and internal energy for photon gas. (DPHY 0)
9. Write a notes on any TWO of the following : (a) Eulerian angles Action - angle variables (c) Classical ideal gas (d) Bose - Einstein condensation. 3 (DPHY 0)
(DPHY 03) M.Sc. DEGREE EXAMINATION, DECEMBER 011. First Year Physics Paper III QUANTUM MECHANICS Time : Three hours Maximum : 100 marks 1. (a) Show that commuting operators have common eigen functions. State and prove Ehrenfest's theorem.. (a) State and explain uncertainty principle. Obtain the solutions of wave equation for a particle moving in three dimensions in a constant potential field with finite walls. 3. (a) Discuss the perturbation of energy states of a normal helium atom. Explain the WKB method for perturbation. 4. (a) Develop the time dependent perturbation theorem. Explain the Einstein transition probabilities based on this theorem.
5. (a) Prove that the operators L and L commute and the operators Lx and Ly do not commute. Obtain the eigen values and eigen vectors of L and Lz operators. 6. (a) Explain the experimental evidence for the existence of electron spin. Obtain the matrices for Jx, Jy and Jz spin operators and discuss their properties. 7. (a) What is Heisenberg picture? Obtain the equation of motion in this picture. Explain the application of Heisenberg picture to harmonic oscillator. 8. (a) Obtain the Schrodirger relativistic equation and give its interpretation. Obtain the Dirac's equation in the presence of Electromagnetic field. 9. Write notes on any TWO of the following : (a) (c) (d) Postulate of quantum mechanics Variation method Wigner-Eckart theorem Dirac matrices. (DPHY 03)
(DPHY 04) M.Sc. DEGREE EXAMINATION, DECEMBER 011. First Year Physics Paper IV ELECTRONICS Time : Three hours Maximum : 100 marks Answer any FIVE of the following. All questions carry equal marks. 1. (a) Explain the working of inverting Op-amp with negative feed back. Discuss the effect of feedback on closed loop gain.. (a) Explain 555 timer and how it generates square wave and triangular wave. Explain the working of Wien bridge oscillator and write down the expression for frequency of oscillation. 3. (a) Discuss the applicability of Maxwell's equation in rectangular wave guides. Explain the working of Klystron. 4. (a) Discuss in detail the generation of AM waves. With the help of block diagram, explain the working of super heterodyne receiver.
5. (a) State and explain De Morgan's theorems. Explain the working of a demultiplexer with a neat diagram. 6. (a) Give the truth tables of RS, JK Flip flops and explain its working. Explain what is meant by multiflexing. 7. (a) Explain the architecture and pin configuration of 8085 p. Write an assembly language program for division of two 8-bit number. 8. (a) Explain the pin configuration of 8086 and discuss the functions of each pin. Write a program to add two 16 bit numbers. 9. Write notes on any TWO of the following : (a) (c) Class B push pull power emplifier. Foster-Seeley discriminator. A/D and D/A converters. (d) Addressing models of 8086. (DPHY 04)