DISTANCE EDUCATION
M.Sc. (Physics) DEGREE EXAMINATION, MAY 2016.
MATHEMATICAL PHYSICS
(2008 onwards)
Time Three hours Maximum 100 marks
Answer any FIVE questions.
Each question carries 20 marks.
20 100)
1. Prove that the eigen values of a hermitian matrix
are real.
Any two eigen vectors corresponding to two distinct
eigen values of a Hermitian matrix are orthogonal.

Diagonalise the matrix






3 5
3
2
3
2
3
4
.
2. Explain orthogonal, unitary and similarity
transformation.
Define a hermitian matrix, orthogonal matrix,
unitary matrix.
Show that the matrix





0 0 1
1 0 0
0 1 0
is an
orthogonal matrix.
If A and B are orthogonal matrixes then
their products are also orthogonal.
Sub. Code
12
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3. Solve Legendre's differential equation
2 0 2
2
2 n n y
dx
x dy
dx
x d y .
Evaluate using Gamma function.

1
0 1 x n
dx

1
0
1 1 xn n
dx .
4. Find finite fourier sine and cosine transforms of the
function f x 2 x 4 .
Find the laplace transform of
eat coswt
eat sinwt .
Using complex variables method show that
5 4 cos 6
2 cos 2
0





d .
5. Given m n
T 2
1 prove that
n mn
j jn g
x
g T
M
x








1 being the metric tensor.
State and prove the convolution theorem in Fourier
transform.
State and prove Taylor's series.
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6. Show by contour integration.






x4 a4 2 2a3
dx for a 0 .
Discuss the vibrations of a Rectangular membrane
and find the solution of the wave equation by
separation of variables.
7. Show that the velocity of a fluid at any point is a
contra variant tensor of rank one.
Derive the moment of inertia of a tensor.
Explain isomorphism and homomorphism.
8. Show that the Kronecker delta is a mixed tensor of
order two.
Explain how tensor analysis is applied to study
stress, strain and Hooke's law.
Explain reducible and irreducible representations in
group theory.