Welcome to the documentation of Pyslise

Pyslise is a Python package (written in C++) to solve Schrödinger equations. In general the time-independent Schrödinger equation is given by:

\[-\nabla^2 \varphi({\bf x}) + V({\bf x}) \varphi({\bf x}) = E \varphi({\bf x})\]

This package implements a constant perturbation (CP) method to efficiently solve the one-dimensional Schrödinger equation:

\[-\frac{d^2}{dx^2}\varphi(x) + V(x) \varphi(x) = E \varphi(x)\]

And also the two-dimensional Schrödinger equation (experimental):

\[-\frac{\partial^2}{\partial x^2}\varphi(x, y) -\frac{\partial^2}{\partial y^2}\varphi(x, y) + V(x, y) \varphi(x, y) = E \varphi(x, y)\]

Besides a python package there is also an interactive web based GUI (compiled with WebAssembly):

• GUI for the one-dimensional problem

(Tested in a recent version of Firefox and Chrome)

Installation

Installing PySlise is as easy as:

pip install pyslise

Make sure you are using a recent 64 bit version of python on a Linux, Windows or macOS (10.15).

Documentation

• Usage examples
  • Using Pyslise
  • Using Pyslise2D
• Reference manual
  • One dimensional (Pyslise)
  • Coupled system (Pyscs)
  • Two dimensional (Pyslise2D)

• Index

Contact

This package is still in its infancy and under active development. So naturally it will not be perfect. When you have questions about the software, come across bugs or have suggestions for improvements, you can always contact us:

Toon Baeyens

toon.baeyens@ugent.be

Ghent University