Give me question paper for MSc Physics examination of Kerala university in PDF file format ?

Here I am giving you question paper for MSc Physics examination of Kerala university in PDF file attached with it so you can get it easily..

1. What are hermitian matrices ? Show that the eigen values of a hermitian matrix are real.

4. Give the generating function for Hermite polynomials and show that
) x ( H n 2 ) x ( H 1 n n −′.
5. Prove the orthogonality of Pn(x).
6. Obtain the Laplace transform of the derivative of a function.
7. Show that the fourier series representation of an even function of x contains only terms of the form ancos nx.

PART – B
Answer all questions. Each question carries ten marks. (3×10=30 Marks)
8. a) Explain orthogonal curvelinear co-ordinates.
b) Derive an expression for the Laplacian in spherical polar co-ordinates.
OR
9. a) Describe the method of separation of variables for solving second order partial
differential equations.
b) Apply the method to the solution of the wave equation in three dimensions.
10. a) Write down Hermite differential equation. Derive Roderigue’s formula for its solution.

11. a) Write down the Legendre differential equation and obtain its solution in the form
of a power series.