DISTANCE EDUCATION
M.Sc. (Physics) DEGREE EXAMINATION, MAY 2017.
MATHEMATICAL PHYSICS
(2008 onwards)
Time Three hours Maximum 100 marks
Answer any FIVE questions.
Each question carries 20 marks.
20 100)
1. Show that any two eigen vectors corresponding to
two distinct eigen values of a Hermitian matrix are
orthogonal to each other.
Diagonalise the matrix






0 0 1
sin cos 0
cos sin 0


.
Prove that the diagonalization of a real symmetric
matrix is orthogonal.
2. Explain about similarity transformation and what
is its physical meaning.
Show that




m n
m n m n

.
Evaluate
1
0 xn
dx using Gamma function.
Sub. Code
12
DE-650
2
SP 5
3. Obtain the solution of Legendre's differential
equation.
Show that x
x
J 2 cos
2
1





.
Prove that
n
n n
n H



2
2 2 1
2 .
4. Find the Laplace transform of
eat coswt, eat sinwt .
State and explain convolution theorem.
Find the solution of two dimensional heat flow
equation.
5. Arrive at the two-dimensional wave equation for
vibrations of a Rectangular Membrane.
Find its solution by the method of separation of
variables.
State and Prove Cauchy's Residue theorem for a
complex function.
6. State and prove Cauchy's integral theorem.
Find the residues of Z4 a4
Zeiz

at its poles.
Use Contour integration to show that






e
dx
x
x x x

cos sin
2 .
DE-650
3
SP 5
7. State and prove that great orthogonality theorem.

Derive the moment on inertia of a tensor.
Explain subgroups and CD sets.
8. Write a note on contraction and metric tensors.
Construct the character table for C3V point group.

Differentiate between Contravariant and covariant
tensors with examples.