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:
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:
Hartree Units: