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Course Dual Degree (B. Tech + Master of Science / Master of Technology)
Semester Sem. VIII
Subject Code PH425
Subject Title Computational Physics

Syllabus

Errors and uncertainties in computations: Types of errors, error in functions, errors in algorithms. Matrix computing and scientific libraries.

Zero-finding and matching: Newton's rule for finding roots. Quantum eigenvalues, particle in a box. Fields due to moving charges.

Integration: Trapezoid rule, Simpson's rule, Gaussian quadrature, multi-dimensional integrals. Monte-Carlo integrations.

Differential equations: Euler's algorithm, Runge-Kutta methods. A forced non-linear oscillator, motion of a charegd particle in an electric field, dynamics of non-linear systems. Numerical solutions of boundary value probems: solution of Laplace equation and Poisson's equation. Heat flow in a meta bar, waves on a string. Born and Eikonal approximations to quantum scattering, partial wave decomposition of the wave function. Solitons. Confined electronic wave packets: time-dependent Schrodinger equation.

Data fitting:Lagrange interpolation, cubic splines, least-square fitting. Fitting exponential decay, fitting heat flow. Non-linear least-squares fitting.

Fourier analysis. Fourier spectral methods. Harmonics in non-linear oscillations. Discrete Fourier transform. Highly non-linear oscillator, Processing noisy signals.

Random walk simulations. Decay simulation, Monte-Carlo simulations. The Ising model, Metropolis algorithm. Molecular dynamics simulations.

Text Books

1. S. E. Koonin, Computational Physics, Westview, 1990.

2. R. H. Landau, M. J. Paez, Computational Physics: Problem Solving with Computers, Wiley-VCH, 2004.

3. H. Gould, J. Tobochnik, W. Christian, An Introduction to Computer Simulation Methods: Applications to Physical Systems, Pearson, Addison-Wesley, 2007.

4. P. L. Devries, J. E. Hasbun, A First Course in Computational Physics, Jones & Bartlett, 2011.

5. J. P. Boyd, Chebyshev and Fourier Spectral Methods, Dover, 2001.

References

Same as References