Computations in quantum mechanics made easy

TL;DR

This paper introduces simple numerical matrix-based techniques for quantum computations, demonstrating their effectiveness in calculating properties of various quantum systems and emphasizing their educational utility.

Contribution

It presents new, easy-to-implement numerical methods for quantum calculations, suitable for teaching and applied to diverse quantum systems.

Findings

Effective for spectral and dynamical calculations

Applicable to single-particle and many-particle systems

Explicit Matlab implementations provided

Abstract

Convenient and simple numerical techniques for performing quantum computations based on matrix representations of Hilbert space operators are presented and illustrated by various examples. The applications include the calculations of spectral and dynamical properties for one-dimensional and two-dimensional single-particle systems as well as bosonic many-particle and open quantum systems. Due to their technical simplicity these methods are well suited as a tool for teaching quantum mechanics to undergraduates and graduates. Explicit implementations of the presented numerical methods in Matlab are given.