Awadhesh Pratap Singh University 2009 M.Sc Physics .%2C Mathematical - Question Paper

M.Sc.(First semester) Physics

Mathematical Physics
Maximum marks:-35

All ques. will carry ½ mark every. Please choose the accurate ans of the followings:-
1.the accurate relation is:-
(a) J-1/2(x)=v2/px sinx
(b) J-1/2(x)=v2/px cotx
(c) J-1/2(x)=v2/px cosx
(d) None of these.
2.Which is correct:-
(a) P3(x)=1/2(5x3-3x)
(b) p3(x)=1/2(3x2-1)
(c) P3(x)=x
(d) P3(x)=1
3.Inverse Laplace transformation of 1/pn is:-
(a)t n-1/n!
(b)t n-1/n+1!
(c)t n+1/n-1!
(d)None of these.
4.Fourier sine transformation of e-x , x>0 is:-
(a)?/?2+1
(b) ?2+1/?
(c)?
(d)2
5.The modulus of the product of 2 complex number|z1 z2| is equal to:-
(a)|z1||z2|
(b)|z2|+|z1|
(c)|z1|-|z2|
(d)|z1|/|z2|
6.The residue of z2/z2+a2 at z+ia is:-
(a) ia
(b) 2ia
(c) 1/2ia
(d) 1/3ia
7.Out of the subsequent functions which is not analytic:-
(a) f(z)=sin hz
(b) f(z)=log hz
(c) f(z)=z2
(d )f(z)=x+iy/x2+y2
8.Laplace trans form of t2sinat is :-
(a) 2a(3p2+a2)/(p2+a2)
(b) 2a(3p2-a2)/(p2+a2)
(c) a(3p2+a2)/(p2+a2)
(d) a(3p2+a2)/(p2+a2)
9.The accurate relation is:-
(a) H2n(0)=(-1) 3n!/n!
(b) H2n(0)=(-1)n 3n!/n!
(c) H2n(0)=(-1) 3n!/2n!
(d)None of the above.
10.The accurate relation is:-
(a)? (x+a)?^n=?_(k=0)^n¦?(n¦k) x^k a^(n-k) ?
(b) f(x)=a_0+?_(n=1)^8¦(a_n cos??npx/L?-b_n sin??npx/L? )
(c) ?_(n=1)^8¦(a_n cos??npx/L?+b_n sin??npx/L? ) =(x+a)n
(d) (x-a)^n=?_(k=0)^n¦?(n¦k) x^k a^(n-k) ?

ans the provided ques. in 100-200 words.All carry two mark each:-

Prove that :-
2n/x Jn()=Jn+1(x) + Jn-1(x)
Or
Pn(x)=1/2n n! dn/dxn(x2-1)2


2.Define finite Fourier sine and cosine transformations with their inverse transformations.
Or
describe Finite Fourier sine and cosine transform of derivatives.
3.Define and discuss the method of determining Green function.
Or
explain non-homogeneous boundary value issues.

4.Prove that the function
U=1/2 log(x2+y2) is harmonic.
Or
Prove that the modulus of sum of 2 complex numbers is always less than or equal to the sum of their modulli.

5.Write short notes on any 2 of the followins:-
(a)Spherical Coordinates
(b)Convolution Theorem
(c)Quantum mechanical scattering issues
(d)Taylors Theorem

ans any 2 of the subsequent in 300-400 words. every ques. carry 10 marks:-

1.Prove that :-
?8^8¦e^(-x2) Hm(x) Hn(x) dx=2n n! v(?) d mn

2.Define and Prove Fourier integral formula.

3.Discuss the Fourier transform method of constructing Green Function.

4.Write Note on the subsequent Topics :-
(a)Curvilinear co-ordinate system
(b)Laplace transform of derivatives and integrals.

Earning:   Approval pending.