The relativistic Schrödinger equation through FFTW 3: An extension of quantumfdtd

•We extend a previous code to solve also the relativistic Schrödinger equation, with a non-exclusive focus on lattice-QCD.•The non-relativistic and the relativistic Schrödinger equation with arbitrary potential is solved in a box.•Solvers: finite-difference time-domain, with Dirichlet boundary conditions; fast fourier transform, with periodic ones.•The different solvers are compared and discretization and finite volume effects are studied.•With lattice-QCD and heavy quarkonia in mind, we focus on small lattices, but large ones were previously tested. In order to solve the time-independent three-dimensional Schrödinger equation, one can transform the time-dependent Schrödinger equation to imaginary time and use a parallelized iterative method to obtain the full three-dimensional eigen-states and eigen-values on very large lattices. In the case of the non-relativistic Schrödinger equation, there exists a publicly available code called quantumfdtd which implements this algorithm. In this paper, we (a) extend the quantumfdtd code to include the case of the relativistic Schrödinger equation and (b) add two optimized Fast Fourier Transform (FFT) based kinetic energy terms for non-relativistic cases. The new kinetic energy terms (two non-relativistic and one relativistic) are computed using the parallelized FFT-algorithm provided by the FFTW 3 library. The resulting quantumfdtd v3 code, which is publicly released with this paper, is backwards compatible with version 2, supporting explicit finite-differences schemes in addition to the new FFT-based schemes. Finally, we (c) extend the original code so that it supports arbitrary external file-based potentials and the option to project out distinct parity eigen-states from the solutions. Herein, we provide details of the quantumfdtd v3 implementation, comparisons and tests of the three new kinetic energy terms, and code documentation. Program Title:quantumfdtd v3 CPC Library link to program files:https://doi.org/10.17632/9p8zyvmdy2.1 Developer's repository link:https://github.com/quantumfdtd/quantumfdtd_v3 Licensing provisions: GPLv3 Programming language:C++, Python, Shell Journal reference of previous version: [1–4] Does the new version supersede the previous version?: Yes Reasons for the new version: We extended the previous version of quantumfdtd, which solves the time-independent non-relativistic three-dimensional Schrödinger equation, to the case of the relativistic kinetic energy. Additionally, we have added th