QuantumFDTD - A computational framework for the relativistic Schrödinger equation

¹ ETSIS de Telecomunicación (UPM), Campus Sur, C/Nikola Tesla, s/n 28031 Madrid, Spain
² INFN-Firenze, Via Giovanni Sansone, 1, 50019 Sesto Fiorentino FI, Italy (moved to UPM)
³ Physik Department, Technische Universität München, James-Franck-Straße 1, D-85748 Garching b. München, Germany
⁴ Leibniz-Rechenzentrum der Bayerischen Akademie der Wissenschaften, Boltzmannstraße 1, D-85748 Garching b. München, Germany
⁵ Department of Physics, Kent State University, Kent, OH 44242 USA
⁶ Institut für Physik & IRIS Adlershof, Humboldt-Universität zu Berlin, Zum Großen Windkanal 6, D-12489 Berlin, Germany

^* e-mail: rafael.delgado@upm.es
^** e-mail: sebastian.steinbeisser@tum.de
^*** e-mail: mstrick6@kent.edu
^**** e-mail: johannes.weber@physik.hu-berlin.de

Published online: 22 December 2022

Abstract

We extend the publicly available quantumfdtd code. It was originally intended for solving the time-independent three-dimensional Schrödinger equation via the finite-difference time-domain (FDTD) method and for extracting the ground, first, and second excited states. We (a) include the case of the relativistic Schrödinger equation and (b) add two optimized FFT-based kinetic energy terms for the non-relativistic case. All the three new kinetic terms are computed using Fast Fourier Transform (FFT).We release the resulting code as version 3 of quantumfdtd. Finally, the code now supports arbitrary external filebased potentials and the option to project out distinct parity eigenstates from the solutions. Our goal is quark models used for phenomenological descriptions of QCD bound states, described by the three-dimensional Schrödinger equation. However, we target any field where solving either the non-relativistic or the relativistic three-dimensional Schrödinger equation is required.