Exploring the Split-Step Method (WIP)

Various simulations of quantum mechanics phenomena using the split-operator method. These are mostly implemented in Python as well as C++/OpenGL.

A rudimentary web-based version of the C++/OpenGL implementation can be found here.

References:

Split-operator method:

• The Arcane Algorithm Archive - Split-operator method
• Wikipedia - Split-step method
• Arxiv - Accelerating the Fourier split operator method via graphics processing units

Overview of methods for soving the nonlinear Schrödinger equation:

• Arxiv - Computational methods for the dynamics of the nonlinear Schrödinger/Gross-Pitaevskii equations

Klein-Gordon equation:

• Wikipedia - Klein-Gordon Equation

Dirac equation:

• Chapter 20 - The Dirac Equation of Principles of Quantum Mechanics by Ramamurti Shankar.
• Wikipedia - Dirac Equation
• Wikipedia - Dirac spinor
• Section II.3 Fourier split operator method for the Dirac equation of Accelerating the Fourier split operator method via graphics processing units

Finding the lowest energy eigenstates using the split-step method:

• Section V.2 Eigenstates of Accelerating the Fourier split operator method via graphics processing units
• 21.2: Imaginary Time Formalism in the final chapter covering path integrals in Principles of Quantum Mechanics.
• Wikipedia - Gram-Schmidt process.

Fourier Transform algorithm for the C++ and OpenGL implementation:

• Wikipedia - Cooley-Tukey Algorithm
• Numerical Recipes Chapter 12

Hartree Units:

• Wikipedia - Hartree atomic units