M. Sc. (Physics):Liquid Crystals:Computational Methods in Physics

First Semester


Classical Mechanics
Statistical Mechanics
Quantum Mechanics
Mathematical Physics
Physics Lab I
Fundamentals of Computer Science and C Programming


Second Semester

Condensed Matter Physics
Experimental Techniques in Physics
Atomic and Molecular Physics
Electrodynamics
Electronics
Physics Lab II


Third Semester

Particle Physics
Nuclear Physics
Semiconductor Physics
Physics Lab III
Seminar


Fourth Semester

Dissertation


Computational Methods in Physics

Fortran 90 Programming: Operating systems, Flow charts, Integer and Floating point arithmetic, built-in functions, Executable and non-executable statements, Assignment, Control and input/output commands, Subroutines and functions, Operation with files, Debugging and testing.

Numerical Algebraic and Transcendental Equations: Methods for determination of zeroes of linear and nonlinear algebraic and transcendental equations, Convergence of solutions, Solution of simultaneous linear equations, Evaluation of numerical determinants, Gaussian elimination and pivoting, Matrix inversion, Iterative methods.

Interpolation and Approximation: Introduction to interpolation, Lagrange approximation, Newton polynomials, Curve fitting by least squares, Polynomial least squares and cubic splines fitting.

Numerical Differentiation and Integration: Numerical differentiation, Quadrature, Simpson’s rule, Gauss’s quadrature formula, Newton – Cotes formula.

Random Variables and Monte Carlo Methods: Random numbers, Pseudo-random numbers, random number generators, Monte Carlo integration: Area of circle, Moment of inertia, Monte Carlo Simulations: Buffen’s needle experiment, Random walk, Importance sampling.

Differential Equations: Euler’s method, Runge Kutta methods, Predictor-corrector methods, Finite difference method, Finite difference equations for partial differential equations and their solution.

Laboratory Assignments: To find mean, standard deviation and frequency distribution of an actual data set from any physics experiment, Wein’s constant using bisection method and false position method.To solve Kepler equation by Newton-Raphson method, Van der Wall gas equation for volume of a real gas by the method of successive approximation. Interpolate a real data set from an experiment using the Lagrange’s method, Newton’s method of forward differences and cubic splines. Fit the Einstein’s photoelectric equation to a realistic data set and hence calculate Plank’s constant. Estimate the value of p by rectangular method, Simpson rule and Gauss quadrature by numerically evaluating any suitable integral.cFind the area of a unit circle by Monte Carlo integration.cTo simulate Buffen’s needle experiment. To simulate the random walk. To study the motion of an artificial satellite by solving the Newton’s equation for its orbit using Euler method. Study the growth and decay of current in RL circuit containing (a) DC source and (b) AC using Runge Kutta method. Draw graphs between current and time in each case. Study the motion of two coupled harmonic oscillators. Compare the numerical results with the analytical results.