Kerala University 2006 M.Sc Physics FIRST SEMESTER - exam paper
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FIRST SEMESTER M.Sc. DEGREE EXAMINATION DECEMBER/JANUARY-06 Branch: - PHYSICS PH 211 - MATHEMATICAL METHODS IN PHYSICS
Time: 3 Hours Max. Marks: 75
PART-A
Answer any five questions. Each question carries 3 marks.
1. Derive the polar form of Cauchy-Riemann equations.
1 - 2
2. Find the inverse of the matrix
1 1
.4 ..2.
3. Find V(j) for the function =2xz -x y at the point (2,-2,-1).
4. If H-cyrl Approve that JsH.nds=0 for any closed surface S.'
5. What are symmetric and anti-symmetric tensors.
6. State the elementary properties of a group. -
7. Find L/1
S(S-a)J
8. Distinguish between binomial and normal distributions.
(5 x 3=15 marks)
' PART-B
Answer all questions. Each question carries 15 marks.
9- a. i. State and prove Cauchys integral formula.
Z4
ii. Find the residue of ---atz=l
(Z-l) (Z-2)(Z-3)
(OR)
i. From the set of vectors (10 1),. (0 0 I) and (1 10). Construct a set of orthogonal vectors.
ii. Find the characteristic equation of the following matrix.
1 2 3 2-14
A
3 1 1
i. Show that J.n(x)-(-1.)" Jn(x)
ii. Show that 2Jni(x)=Jn.i(x)-Jn+](x)
(OR)
Derive the Bessels differentiating equation and hence obtain Bessels function of Zeroth order.
i. Find the Fourier inverse sine transform of e'Xn.
ii. Find the Laplace Transform of Sinhat and Coshat.
(OR)
i. Show that for a finite group G, every representation is equivalent to a unitary representation.
ii. Show that order of any element of a group is always equal to the order of its inverse.
(3 x 15=45 marks)
PART -C
Answer any three questions. Each question carries 5 marks.
Show that every orthononnal set of vectors is linearly independent.
Find Z/'i---1 '
[ 52 + 9 J
Show that Sjj is not a tensor.
Explain Lie groups.
What are the characteristics of poissons distribution?
If u=x2yz, v=xy-3z2. Find V.[(Vu).(Vu)]
(3x5 = 15 marks)
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