Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2004.10046

Web-Schrödinger: Program for the interactive solution of the time dependent and stationary two dimensional (2D) Schr{ö}dinger equation

Géza I. Márk

Published Apr 18, 2020• 1 citation
arXivHTMLPDF

Abstract

Web-Schr{ö}dinger is an interactive client-server software for the solution of the time-dependent and time-independent (stationary) Schr{ö}dinger equation. The program itself runs on a server computer and can be used through the Internet with a simple Web browser. Nothing is installed on the user's computer. The user can load, run, and modify ready-made example files, or prepare her/his own configuration(s), which can be saved on her/his own computer for later use. Several users can access the program parallelly and each can have independent sessions. Typical run times are in the second, or minute range.

DOI
10.48550/arxiv.2004.10046

Related papers

A general procedure for solving the time-dependent Schr$ouml$dinger equation

Chuyi Chen

A nonperturbative procedure for solving the time-dependent Schrödinger equation, called the multi-projection approach or phase dynamics of quantum mechanics, is derived and illustrated. With the help of this new procedure, time-dependent quantum systems become generally solvable (if corresponding stationary systems are solvable) and the phase character of quantum mechanics reveals itself very clearly.

Journal of Physics A Mathematical and General•Jul 25, 2002•1 citation

Computer graphics for solutions of time-dependent Schrödinger equations

Robert L. W. Chen

Computer graphics has been developed as a teaching aid for an undergraduate course in quantum mechanics. It has the following capabilities: (1) it solves the time-dependent Schrödinger equation and displays the results; (2) the user may interact with the computer program by choosing the initial condition of the wave function, the potential V(x), etc; and (3) it works reasonably fast on computer facilities available in most of the large- and medium-sized colleges and universities.

American Journal of Physics•Oct 1, 1982•8 citations

Time‐dependent and time‐independent Schrö dinger equations

Nils O. Petersen

The Time‐Dependent Schrödinger Equation (TDSE) is provided in Postulate V as the means whereby the wave functions can be determined. This requires that the Hamiltonian Operator can be defined. In general, the Hamiltonian can be a complex function of position and time (some examples will be provided later), but we will proceed with some constraints on the potential energy term, which simplifies the problem substantially.

CRC Press eBooks•Apr 7, 2017•0 citations

Explicit Magnus expansions for solving the time-dependent Schrödinger equation

Ochbadrakh Chuluunbaatar, Vladimir Leonardovich Derbov, Artbazar Galtbayar +4 more

The symmetric implicit operator-difference multi-layer schemes for solving the time-dependent Schr?dinger equation based on decomposition of the evolution operator via the explicit Magnus expansion up to the sixth order of accuracy with respect to the time step are presented. Reduced schemes for solving the set of coupled time-dependent Schr?dinger equations with respect to the hyper-radial variable are devised by using the Kantorovich expansion of the wave packet over a set of appropriate parametric basis angular functions. Further discretization of the resulting problem with symmetric operators is implemented by means of the finite-element method. The convergence and efficiency of the numerical schemes are demonstrated in benchmark calculations of the exactly solvable models of a one-dimensional time-dependent oscillator, a two-dimensional oscillator in time-dependent electric field by using the conventual angular basis, and the inexactly solvable model of a three-dimensional kicked hydrogen atom in a magnetic field by using a parametric basis of the angular oblate spheroidal functions developed in our previous paper (Chuluunbaatar O et al 2007 J. Phys. A: Math. Theor. 40 11485?524).

Journal of Physics A Mathematical and Theoretical•Jun 26, 2008•12 citations

Program for quantum wave-packet dynamics with time-dependent potentials (new version announcement)

Claude M. Dion

wavepacket is a program to simulate the dynamics of a wave packet interacting with a time-dependent potential, with the time-dependent Schrödinger equation being solved on a one-, two-, or three-dimensional spatial grid using the split operator method. This new version fixes bugs present in the original program. Program Title: wavepacket CPC Library link to program files: https://doi.org/10.17632/gnxmkygxrw.1 Licensing provisions: GPLv3 Programming language: C (iso C99) Journal reference of previous version: Comput. Phys. Commun. 185 (2014) 407–414. Does the new version supersede the previous version?: Yes Reasons for the new version: Bug fixes. Summary of revisions: This new version fixes bugs in the program wavepacket [1]. In the original version, the function print_wf_bin, used (optionally) to write out the wave function as a binary file, contained a bug that would result in only part of the full wave function being written out when the program was run in parallel. Additionally, negative values of the parameters nt and/or nprint could lead to the program being stuck in an infinite loop. Additional checks have been added to ensure that both these parameters are positive (or zero). Nature of problem: Solves the time-dependent Schrödinger equation for a single particle interacting with a time-dependent potential. Solution method: The wave function is described by its value on a spatial grid and the evolution operator is approximated using the split-operator method [2,3], with the kinetic energy operator calculated using a Fast Fourier Transform. Additional comments including restrictions and unusual features: Simulation can be in one, two, or three dimensions. The fftw [4] implementation of the fast Fourier transform is used, so the corresponding library must be installed. Serial and parallel versions are compiled from the same source files. The parallel version is based on the Message-Passing Interface (mpi) [5]. C.M. Dion, A. Hashemloo, G. Rahali, Comput. Phys. Commun. 185 (2014) 407–414. M.D. Feit, J.A. Fleck, Jr., A. Steiger, Solution of the Schrödinger equation by a spectral method, J. Comput. Phys. 47 (1982) 412–433. M.D. Feit, J.A. Fleck, Jr., Solution of the Schrödinger equation by a spectral method II: Vibrational energy levels of triatomic molecules, J. Chem. Phys. 78 (1) (1983) 301–308. http://www.fftw.org http://www.mpi-forum.org

Computer Physics Communications•Jun 15, 2023•0 citations

An user-friendly software tool for the solution of the time-dependent Schrödinger and Gross-Pitaevskii equations

Thomas Serafini, Andrea Bertoni

In this work we present TDStool, a general-purpose easy-to-use software tool for the solution of the time-dependent Schrödinger equation in 2D and 3D domains with arbitrary time-dependent potentials. The numerical algorithms adopted in the code, namely Fourier split-step and box-integration methods, are sketched and the main characteristics of the tool are illustrated. As an example, the dynamics of a single electron in systems of two and three coupled quantum dots is obtained. The code is released as an open-source project and has a build-in graphical interface for the visualization of the results.

Journal of Physics Conference Series•Nov 1, 2009•1 citation
Web-Schr{ö}dinger is an interactive client-server software for the solution of the time-dependent and time-independent (stationary) Schr{ö}dinger equation. The program itself runs on a server computer and can be used through the Internet with a simple Web browser. Nothing is installed on the user's computer. The user can load, run, and modify ready-made example files, or prepare her/his own configuration(s), which can be saved on her/his own computer for later use. Several users can access the program parallelly and each can have independent sessions. Typical run times are in the second, or minute range.
A general procedure for solving the time-dependent Schroumloumloumldinger equation
The symmetric implicit operator-difference multi-layer schemes for solving the time-dependent Schr?dinger equation based on decomposition of the evolution operator via the explicit Magnus expansion up to the sixth order of accuracy with respect to the time step are presented. Reduced schemes for solving the set of coupled time-dependent Schr?dinger equations with respect to the hyper-radial variable are devised by using the Kantorovich expansion of the wave packet over a set of appropriate parametric basis angular functions. Further discretization of the resulting problem with symmetric operators is implemented by means of the finite-element method. The convergence and efficiency of the numerical schemes are demonstrated in benchmark calculations of the exactly solvable models of a one-dimensional time-dependent oscillator, a two-dimensional oscillator in time-dependent electric field by using the conventual angular basis, and the inexactly solvable model of a three-dimensional kicked hydrogen atom in a magnetic field by using a parametric basis of the angular oblate spheroidal functions developed in our previous paper (Chuluunbaatar O et al 2007 J. Phys. A: Math. Theor. 40 11485?524).
wavepacket is a program to simulate the dynamics of a wave packet interacting with a time-dependent potential, with the time-dependent Schrödinger equation being solved on a one-, two-, or three-dimensional spatial grid using the split operator method. This new version fixes bugs present in the original program. Program Title: wavepacket CPC Library link to program files: https://doi.org/10.17632/gnxmkygxrw.1 Licensing provisions: GPLv3 Programming language: C (iso C99) Journal reference of previous version: Comput. Phys. Commun. 185 (2014) 407–414. Does the new version supersede the previous version?: Yes Reasons for the new version: Bug fixes. Summary of revisions: This new version fixes bugs in the program wavepacket [1]. In the original version, the function print_wf_bin, used (optionally) to write out the wave function as a binary file, contained a bug that would result in only part of the full wave function being written out when the program was run in parallel. Additionally, negative values of the parameters nt and/or nprint could lead to the program being stuck in an infinite loop. Additional checks have been added to ensure that both these parameters are positive (or zero). Nature of problem: Solves the time-dependent Schrödinger equation for a single particle interacting with a time-dependent potential. Solution method: The wave function is described by its value on a spatial grid and the evolution operator is approximated using the split-operator method [2,3], with the kinetic energy operator calculated using a Fast Fourier Transform. Additional comments including restrictions and unusual features: Simulation can be in one, two, or three dimensions. The fftw [4] implementation of the fast Fourier transform is used, so the corresponding library must be installed. Serial and parallel versions are compiled from the same source files. The parallel version is based on the Message-Passing Interface (mpi) [5]. C.M. Dion, A. Hashemloo, G. Rahali, Comput. Phys. Commun. 185 (2014) 407–414. M.D. Feit, J.A. Fleck, Jr., A. Steiger, Solution of the Schrödinger equation by a spectral method, J. Comput. Phys. 47 (1982) 412–433. M.D. Feit, J.A. Fleck, Jr., Solution of the Schrödinger equation by a spectral method II: Vibrational energy levels of triatomic molecules, J. Chem. Phys. 78 (1) (1983) 301–308. http://www.fftw.org http://www.mpi-forum.org
In this work we present TDStool, a general-purpose easy-to-use software tool for the solution of the time-dependent Schrödinger equation in 2D and 3D domains with arbitrary time-dependent potentials. The numerical algorithms adopted in the code, namely Fourier split-step and box-integration methods, are sketched and the main characteristics of the tool are illustrated. As an example, the dynamics of a single electron in systems of two and three coupled quantum dots is obtained. The code is released as an open-source project and has a build-in graphical interface for the visualization of the results.