Estimate the kinetic energy of the neutrons in a neutron beam that can be used to probe lattice structures with an interatomic spacing of 0.3 nm. The mass of the neutron is 1.675 x 10-27 kg.
See Answer →Show that in the x - y plane, a rotation about the origin in an anti-clockwise
direction by an angle φ will move the points (x, y) to 
by the matrix
Obtain all the proper subgroups of the permutation groups S3 = {e,p1...,p5 }and their cosets.
Given:
Construct the multiplication table for the group of permutations of {1,2,3}.
See Answer →A metal plate covering the first quadrant of the xy plane has its edge along y-axis insulated. The edge along x-axis is held at an initial temperature
Obtain the steady state temperature distribution as a function of x and y.
See Answer →Obtain the images of the line x = 0 and y = 0 under the transformation w = z2 and prove that they intersect at right angles.
See Answer →Write the Laurent series expansion of ez/ (z-1)2 singularity and the region of convergence. about z = 1. Determine the type of
See Answer →Show that the series converges for IzI < 2 and find its sum.
Define contravariant and covariant tensors of rank 2. Prove that vi = gijaj transform contravariantly.
See Answer →Obtain the eigenvalues and the orthonormal eigenvectors for the following real symmetric matrix:
Show that the set of all 2x2 Hermitian matrices form a four dimensional real vector space. Obtain a suitable basis for this vector space.
See Answer →What are orthonormal vectors? Show that two non-null, orthogonal vectors are linearly independent.
See Answer →Write an expression for generating function for Hermite polynomials. Using this expression evaluate the integral
Using the Rodrigue's formula of Legendre polynomials, obtain the values of P3(x) and P4(x).
See Answer →Using the generating function for Bessel functions of the first kind and integral order, obtain the recurrence relation
The Helmholtz equation in Cartesian coordinates can be written as
Reduce it to three ODEs.
See Answer →