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Quantum Many-Body Simulations in Haskell

Abstract

Applying numerical methods in quantum mechanics has always been necessary in analyzing complex structures of quantum mechanical systems. The technical progress of computer performance has enabled physicists and mathematicians to simulate complex many-body systems. With these methods tangible progress in quantum physics can be made, to analyze quantum phenomena on the level of many-particle interactions. This article focuses on the implementation of numerical methods for many-body simulation in the functional programming language Haskell . Functional programming languages get more and more interesting for physicists through their mathematical way of implementation. In this article simple quantum systems are simulated first and an overview of different numerical methods for solving the Schrödinger equation will be given following an attempt to proceed to many-body systems from simple quantum systems.

To Do List

Chapter 1

• method of finite differences in
  • 1D
  • 2D
  • 3D
• comparison with analytic results
• other possible methods to solve the SRE numerically

Chapter 2

• introduction to the problem
• Hartree-Fock method and equations
• the Roothaan equation
• overview of the implementations
• implementation
• results
• comparison
• possible improvements

Implementation

• parse Data from The python EMSL API to the programm

• store Data in suitable data types

• functions for integrals involving gaussians

• functions for creating important matrices, e.g.:

  • S-matrix
  • h-matrix
  • Coeff-matrix
  • etc

  And most important:

• Hartree-Fock self consistency calculation