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

Natural Science Journal of Xiangtan University

Application of Matlab in Molecular Dynamics:The Time-Dependent Evolution of Wavepacket via Matlab

Min Cun-gao

Published Jan 1, 2011• 0 citations
OpenAlex

Abstract

The time-dependent evolution of wave packet is calculated in several model potential(such as one dimensional barrier potential,hamonic oscillator potential and double well potential) by using Matlab language.It is demonstrated that Matlab is a powerful language for calculating the molecular time-dependent dynamics.The program is universal.User only need a little modification to calculate the real molecular time-dependent evolution.

Related papers

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

Simple approach to the time evolution of wave packets in a harmonic oscillator potential

Qiong-Gui Lin

A simple approach is presented to calculate the explicit time dependent wave functions of some wave packets in a harmonic oscillator potential. In this approach no knowledge on special functions is needed.

College Physics•Jan 1, 2003•0 citations

A strategy for time dependent quantum mechanical calculations using a Gaussian wave packet representation of the wave function

Shin‐ichi Sawada, Robert Heather, Bret Jackson +1 more

We develop methodology for performing time dependent quantum mechanical calculations by representing the wave function as a sum of Gaussian wave packets (GWP) each characterized by a set of parameters such as width, position, momentum, and phase. The problem of computing the time evolution of the wave function is thus reduced to that of finding the time evolution of the parameters in the Gaussians. This parameter motion is determined by minimizing the error made by replacing the exact wave function in the time dependent Schrödinger equation with its Gaussian representation approximant. This leads to first order differential equations for the time dependence of the parameters, and those describing the packet position and the momentum of each packet have some resemblance with the classical equations of motion. The paper studies numerically the strategy needed to achieve the best GWP representation of time dependent processes. The issues discussed are the representation of the initial wave function, the numerical stability and the solution of the differential equations giving the evolution of the parameters, and the analysis of the final wave function. Extensive comparisons are made with an approximate method which assumes that the Gaussians are independent and their width is smaller than the length scale over which the potential changes. This approximation greatly simplifies the calculations and has the advantage of a greater resemblance to classical mechanics, thus being more intuitive. We find, however, that its range of applications is limited to problems involving localized degrees of freedom that participate in the dynamic process for a very short time. Finally we give particular attention to the notion that the GWP representation of the wave function reduces the dynamics of one quantum degree of freedom to that of a set of pseudoparticles (each represented by one packet) moving according to a pseudoclassical (i.e., classical-like) mechanics whose ‘‘phase space’’ is described by a position and momentum as well as a complex phase and width.

The Journal of Chemical Physics•Sep 15, 1985•205 citations

Time-Dependent Wave Packet Dynamics Calculations of Cross Sections for Ultracold Scattering of Molecules

Jiayu Huang, Shu Liu, Dong Hui Zhang +1 more

Because the de Broglie wavelength of ultracold molecules is very large, the cross sections for collisions of molecules at ultracold temperatures are always computed by the time-independent quantum scattering approach. Here, we report the first accurate time-dependent wave packet dynamics calculation for reactive scattering of ultracold molecules. Wave packet dynamics calculations can be applied to molecular systems with more dimensions and provide real-time information on the process of bond rearrangement and/or energy exchange in molecular collisions. Our work thus makes possible the extension of rigorous quantum calculations of ultracold reaction properties to polyatomic molecules and adds a new powerful tool for the study of ultracold chemistry.

arXiv:1710.09057•Physical Review Letters•Apr 4, 2018•44 citations

A note on the application of the semiclassical wave packet dynamics

Michal Kolář, M. K. Ali, S. F. O’Shea

The optimal choice of the initial parameters of the Gaussian wave packets in the time dependent quantum mechanical calculations using a Gaussian wave packet representation of the wave function is discussed. The proposed procedure is illustrated with the simple case of one dimensional scattering and the propagation of the ground state of the Morse potential.

The Journal of Chemical Physics•Jan 15, 1989•2 citations

Simulation of Time-Independent Aharanov-Bohm Effect Using Matlab

Wang Lepeng, Tan EngLeong, Nan Wang

We simulated time-varying Aharanov-Bohm effect (ABE) under time-independent magnetic field using Matlab, taking into account the influence of time-varying magnetic field on charged particles moving in a two-dimensional plane. According to our models, we discovered the time evolution of wave function and interference patterns. We also developed two mathematical models to analyze this phenomenon, of which the first mode focuses on the time evolution of the wave function, governed by the time-dependent Schrödinger equation incorporating electromagnetic potentials, while the second one is responsible for simulating the resulting interference patterns by modifying the intensity of wave packet based on the frequency-dependent phase shift caused by the sinusoidal magnetic field in the solenoid. Our results align with theoretical expectations and provide new insights into the frequency-dependent nature of the time-varying ABE.

Industry science and engineering.•Dec 1, 2024•0 citations
The time-dependent evolution of wave packet is calculated in several model potential(such as one dimensional barrier potential,hamonic oscillator potential and double well potential) by using Matlab language.It is demonstrated that Matlab is a powerful language for calculating the molecular time-dependent dynamics.The program is universal.User only need a little modification to calculate the real molecular time-dependent evolution.
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
We develop methodology for performing time dependent quantum mechanical calculations by representing the wave function as a sum of Gaussian wave packets (GWP) each characterized by a set of parameters such as width, position, momentum, and phase. The problem of computing the time evolution of the wave function is thus reduced to that of finding the time evolution of the parameters in the Gaussians. This parameter motion is determined by minimizing the error made by replacing the exact wave function in the time dependent Schrödinger equation with its Gaussian representation approximant. This leads to first order differential equations for the time dependence of the parameters, and those describing the packet position and the momentum of each packet have some resemblance with the classical equations of motion. The paper studies numerically the strategy needed to achieve the best GWP representation of time dependent processes. The issues discussed are the representation of the initial wave function, the numerical stability and the solution of the differential equations giving the evolution of the parameters, and the analysis of the final wave function. Extensive comparisons are made with an approximate method which assumes that the Gaussians are independent and their width is smaller than the length scale over which the potential changes. This approximation greatly simplifies the calculations and has the advantage of a greater resemblance to classical mechanics, thus being more intuitive. We find, however, that its range of applications is limited to problems involving localized degrees of freedom that participate in the dynamic process for a very short time. Finally we give particular attention to the notion that the GWP representation of the wave function reduces the dynamics of one quantum degree of freedom to that of a set of pseudoparticles (each represented by one packet) moving according to a pseudoclassical (i.e., classical-like) mechanics whose ‘‘phase space’’ is described by a position and momentum as well as a complex phase and width.
Because the de Broglie wavelength of ultracold molecules is very large, the cross sections for collisions of molecules at ultracold temperatures are always computed by the time-independent quantum scattering approach. Here, we report the first accurate time-dependent wave packet dynamics calculation for reactive scattering of ultracold molecules. Wave packet dynamics calculations can be applied to molecular systems with more dimensions and provide real-time information on the process of bond rearrangement and/or energy exchange in molecular collisions. Our work thus makes possible the extension of rigorous quantum calculations of ultracold reaction properties to polyatomic molecules and adds a new powerful tool for the study of ultracold chemistry.
We simulated time-varying Aharanov-Bohm effect (ABE) under time-independent magnetic field using Matlab, taking into account the influence of time-varying magnetic field on charged particles moving in a two-dimensional plane. According to our models, we discovered the time evolution of wave function and interference patterns. We also developed two mathematical models to analyze this phenomenon, of which the first mode focuses on the time evolution of the wave function, governed by the time-dependent Schrödinger equation incorporating electromagnetic potentials, while the second one is responsible for simulating the resulting interference patterns by modifying the intensity of wave packet based on the frequency-dependent phase shift caused by the sinusoidal magnetic field in the solenoid. Our results align with theoretical expectations and provide new insights into the frequency-dependent nature of the time-varying ABE.