/My-Computational-Physics

A repository having all my physics and math programs.

Primary LanguageJupyter NotebookGNU General Public License v2.0GPL-2.0

My Computational Physics Repository

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Introduction and Motivation

This repository explores a diverse range of physics and math concepts, focusing on simulations, programs, and $\LaTeX$. Utilizing Python and $\LaTeX$ throughout, my primary motivation was to implement physics and math concepts on a computer after completing relevant Udemy courses and consulting helpful online resources, which are listed at the end.

Project Lists and Details

Python Projects

  1. Project-1: Series Expansion, Interpolation, and Curve Fitting

    • Taylor series
    • Taylor series expansion
    • Interpolation, Splines, curve fitting
    • Error calculations

  2. Project-2: Derivatives

    • Derivatives of math functions
    • Central difference method
    • Richardson's method
    • Multi-dimensional derivatives (gradient, divergence, and curl)

  3. Project-3: Integrals

    • Discretizing integrals and trapezoidal rule
    • Improving accuracy: Simpson's rule
    • Rotational Energy and Moment of inertia
    • Analyzing periodic signals via Fourier Transforms

  4. Project-4: Differential Equations-I

    • Euler's method
    • Time-amplified radioactive decay
    • Higher order differential equations
    • Free fall, Pendulum, Damping and driving forces
    • Scipy Introduction and higher order differential equations
    • Runge Kutta $4^{th}$ order method

  5. Project-5: Differential Equation-II

    • Simulating a rolling ball-Two decoupled oscillator
    • Chaos and Lorentz systems
    • Heat Equation
    • 3-body problem: Coupled differential equation for sun, earth, and moon
    • Rocketship

  6. Project-6: Eigen-value Problem

    • 3-coupled oscillators: Equation of motion
    • Analyzing the eigen-modes of the 3-coupled oscillators
    • Fit 3 harmonic oscillators to the numerical solution
    • Generalization to n-coupled oscillator

  7. Project-7: Monte Carlo algorithms & Magnets

    • Calculating $\pi$ using Monte Carlo algorithm
    • Simulating a magnet

  8. Project-8: Quantum Mechanics - Solving Schrodinger wave equation

    • Particle in a box
    • Quantum harmonic oscillator
    • Spherical harmonics
    • Quantum tunneling effect

  9. Project-9: Electronic Properties of Graphene

    • Free electron to band structures
    • Plotting graphene lattice
    • Band structure of graphene
    • Dirac points and massless electrons
    • Plotting a graphene nano-ribbon
    • Applying magnetic field: Landau quantization & Quantum Hall Effect
    • Moire lattice of twisted bilayers of graphene

  10. Project-10: Quantum visualization using python's qmsolve.

  11. Projecct-11:Basics of Linear Algebra

$\LaTeX$ Projects and Documents

Inspiration and Resources

  1. Computational Physics: Scientific Programming with Python
  2. Master Math by Coding in Python
  3. Mr. P Solver
  4. Statistical Mechanics: Algorithms and Computations