Computational-Physics (under construction)

Collaborators are welcome, mail: chinmaykhasanis@gmail.com. This repository contains the following.

Numerical methods

• Initial and Boundary value problems (ODE solvers): Euler, Runge Kutta, Shooting methods. Numerical Integration: Trapezoidal, Quadrature, Newton-Cotes, Gaussian Quadrature.

Classical

• Pendulum
• Simulating Magnus effect for boundary value problem.

Quantum

• 1D Time independent Schrodinger equation solution: Numerov-Cooley algorithm, The Matching Point method, Finite difference method (exact diagonalisation), finite Basis method.
• Computation of first N Eigenstates
• Variational Method: Ground state for non-overlapping and Overlapping basis.
• Time dependent Schrodinger equation: Unitary Propagation Operator- Euler, Crank-Nicholson approximation, Direct Time Discretisation.

Statistical

• Simulating Random walk for absorbing and reflecting boundary conditions.
• Monte-Carlo methods: MC integration, Importance sampling , Metropolis Monte-Carlo algorithm.
• 2D Ising Model simulation using Metropolis Monte-Carlo method: Calculating average magnetization, Magnetic susceptibility, Specific heat, Critical Point.

References:

1. Press, W. H. (2007). Numerical recipes 3rd edition: The art of scientific computing. Cambridge university press.
2. Giordano, N. J. (2012). Computational physics. Pearson Education India.
3. Izaac, J., & Wang, J. (2018). Computational Quantum Mechanics. Berlin: Springer.
4. Thijssen, J. (2007). Computational Physics. Cambridge university press.
5. Frenkel, D., & Smit, B. (2023). Understanding molecular simulation: from algorithms to applications. Elsevier.
6. Allen, M. P., & Tildesley, D. J. (2017). Computer simulation of liquids. Oxford university press.