WavePacket: A Matlab package for numerical quantum dynamics. I: Closed quantum systems and discrete variable representations

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• 作者：Burkhard Schmidt^a ; ^{burkhard.schmidt@fu-berlin.de} ; Ulf Lorenz^b ; ^{ulf@wavepacket.org}
• 关键词：Schrö ; dinger equation ; Quantum dynamics ; Numerical propagation ; Bound states ; Discrete variable representation ; Non-adiabatic transitions
• 刊名：Computer Physics Communications
• 出版年：2017
• 出版时间：April 2017
• 年：2017
• 卷：213
• 期：Complete
• 页码：223-234
• 全文大小：1137 K
• 卷排序：213

文摘

WavePacket is an open-source program package for the numerical simulation of quantum-mechanical dynamics. It can be used to solve time-independent or time-dependent linear Schrödinger and Liouville–von Neumann-equations in one or more dimensions. Also coupled equations can be treated, which allows to simulate molecular quantum dynamics beyond the Born–Oppenheimer approximation. Optionally accounting for the interaction with external electric fields within the semiclassical dipole approximation, WavePacket can be used to simulate experiments involving tailored light pulses in photo-induced physics or chemistry. The graphical capabilities allow visualization of quantum dynamics ‘on the fly’, including Wigner phase space representations. Being easy to use and highly versatile, WavePacket is well suited for the teaching of quantum mechanics as well as for research projects in atomic, molecular and optical physics or in physical or theoretical chemistry. The present Part I deals with the description of closed quantum systems in terms of Schrödinger equations. The emphasis is on discrete variable representations for spatial discretization as well as various techniques for temporal discretization. The upcoming Part II will focus on open quantum systems and dimension reduction; it also describes the codes for optimal control of quantum dynamics. The present work introduces the MATLAB version of WavePacket 5.2.1 which is hosted at the Sourceforge platform, where extensive Wiki-documentation as well as worked-out demonstration examples can be found.Program summaryProgram Title: WavePacketProgram Files doi:http://dx.doi.org/10.17632/tc5mrhx9sb.1Licensing provisions: GPLv3Programming language:MatlabNature of problem:Schrödingerś equations are of fundamental importance in non-relativistic quantum mechanics of distinguishable particles. The solutions of the time-independent equation (TISE) are wavefunctions in coordinate space, the absolute squares of which are usually interpreted as probability density. The time-dependent equation (TDSE) describes the dynamics of a quantum system evolving in time. It plays a crucial role for the simulation, understanding, and prediction of modern experiments in atomic, molecular and optical physics where systems are driven by temporally shaped external fields.Solution method:All numerical methods compiled in WavePacket are based on discrete variable representations. Currently implemented are Gauss–Hermite, Gauss–Legendre and FFT-based schemes. The TISE is solved either by direct diagonalization or by propagation in imaginary time. For the TDSE there is a choice between second order differencing, operator splitting and Chebychev polynomial methods.Additional comments including Restrictions and Unusual features:The WavePacket program package is rather easy and intuitive to use, providing visualization of quantum dynamics ‘on the fly’. It is mainly intended for low-dimensional systems, typically not exceeding three to five degrees of freedom. Detailed user guides and reference manuals are available through numerous Wiki pages hosted at the SourceForge platform where also a large number of well documented demonstration examples can be found.