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