Mathematical Physics and Special Theory of Relativity
B.Sc. pt II course
B.Sc. pt II course
Dates and timings: Monday and Tuesday, 08:00 AM – 09:00 AM
Starting date: Revision of pre-requisites from July 27, new course material from August 10, 2015
Course started in July 2015 and ended in January 2016. Now this page is archived.
Orthogonal Curvilinear co-ordinate system. Scale factors, expression for gradient, divergence and curl and their applications to Cartesian, circular, cylindrical and spherical polar co-ordinate.
Co-ordinate transformation and Jacobian. Transformation of Covariant, Contravariant and Mixed Tensors. Addition, Multiplication and Contraction of Tensors. Metric tensor and its use in transformation of tensors.
Dirac Delta Function and its properties.
Lorentz transformation and rotation in space-time like and space like vector, world line, macro-causality.
Four vector formulation, energy momentum four vector, relativistic equation of motion, invariance of rest mass, orthogonality of four force and four velocity. Lorentz force as an example of four force, transformation of four frequency vector, longitudinal and transverse Doppler's effect.
Transformation between laboratory and center of mass system, four momentum conservation, kinematics of decay products of unstable particles and reaction thresholds: Pair production, inelastic collision of two particles, Compton effect.
(A) Transformation of electric and magnetic fields between two inertial frames.
(B) The second order linear differential equation with variable coefficient and singular points, series solution method and its application to the Hermite's. Legendre's and Laguerre's differential equations; Basic properties like orthogonality, recurrence relation, graphical represntation and generating function of Hermite, Lagendre, Leguerre and Associated Legendre function (simple applications).
Techniques of separation of variables and its application to following boundary value problems. (i) Laplace equation in three dimensional Cartesian coordinate system-line charge between two earthed parallel plates. (ii) Helmholtz equation in circular cylindrical coordinates-cylindrical resonant cavity, (iii) Wave wquation in spherical polar coordinates the vibrations of a circular membrane, (iv) Diffusion equation in two dimensional Cartesian coordinate system, heat conduction in thin rectangular plate, (v) Laplace equation in spherical coordinate system- electric potential around a spherical surface.