A fast and simple program for solving local Schrödinger equations in two and three dimensions

Abstract

We describe a simple and rapidly converging code for solving local Schrödinger equations in two and three dimensions. Our method utilizes a fourth-order factorization of the imaginary time evolution operator which improves the convergence rate by one to two orders of magnitude compared with a second-order Trotter factorization. We present the theory behind the method and strategies for assessing convergence and accuracy. Our code requires one user defined function which specifies the local external potential. We describe the definition of this function as well as input and output functionalities. Program summary Program title: 3dsch/2dsch Catalogue identifier: AEAQ_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEAQ_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 40 085 No. of bytes in distributed program, including test data, etc.: 285 957 Distribution format: tar.gz Programming language: Fortran 90 Computer: Tested on x86, amd64, Itanium2, and MIPS architectures. Should run on any architecture providing a Fortran 90 compiler Operating system: So far tested under UNIX/Linux and Irix. Any OS with a Fortran 90 compiler available should suffice RAM: 2 MB to 16 GB, depending on system size Classification: 6.10, 7.3 External routines: FFTW3 ( http://www.fftw.org/), Lapack ( http://www.netlib.org/lapack/) Nature of problem: Numerical calculation of low-lying states of 2D and 3D local Schrödinger equations in configuration space. Solution method: 4th order factorization of the diffusion operator. Restrictions: The code is at this time designed for up to 152 states in 3D and for up to 100 states in 2D. This number can easily be increased by generating more trial states in the initialization routine. Additional comments: Sample input files for the 2D and the 3D version as well as a gnuplot script for assessing convergence are included in the distribution. Running time: Seconds to hours, depending on system size. The test runs provided with the package take only a few seconds to run.