Numerical quantum dynamics using WavePacket 4

PID (if applicable): doi:10.1016/j.cpc.2016.12.007

Problem Statement

Solve Schrödingers equations

Object of Research and Objective

Solve Schrödingers equations

Procedure

Although WavePacket is made for general quantum systems, so far it has been developed/used mainly for describing the dynamics of molecules, i.e., typically the motion of the comprising nuclei. Especially when low masses (e.g. hydrogen atoms), low energies, and/or low temperatures are involved, the dynamics of the nuclei may be subject to quantum effects. Hence, the modeling of small molecules should be based on quantum mechanical modeling. Because of the computational effort increasing steeply (exponentially?) with the number of atoms, this can not be done for large molecules.

Involved Disciplines

Mathematical Areas:

1 - partial differential equation
2 - Schrödinger equation

Non-Mathematical Disciplines:

1 - quantum mechanics

Data Streams

wave functions

Model

ID: mardi:Q56

time-independent Schrödinger equation

eigenvalue equation for the Hamiltonian operator

Discretization

• Time:
• Space: Fourier/Plane wave

Variables

Name	Unit	Symbol
Energy	J	E
Hamiltonian	J	${\textstyle {\hat {H}}}$
Quantum Number	dimensionsless	n
Quantum State	${\textstyle 1/{\sqrt {(}}length)}$	${\textstyle \psi }$

Parameters

Name	Unit	Symbol

Process Information

Process Steps

Name	Description	Input	Output	Method	Parameter	Environment	Mathematical Area

Applied Methods

ID	Name	Process Step	Parameter	implemented by
mardi:Q57	diagonalization			WavePacket

Software used

ID	Name	Description	Version	Programming Language	Dependencies	versioned	published	documented
mardi:Q59	WavePacket	Numerical Quantum Dynamics	7.2.1	MatLab		Yes	Yes	Yes

Hardware

ID	Name	Processor	Compiler	#Nodes	#Cores

Input Data

ID	Name	Size	Data Structure	Format Representation	Format Exchange	binary/text	proprietary	to publish	to archive

Output Data

ID	Name	Size	Data Structure	Format Representation	Format Exchange	binary/text	proprietary	to publish	to archive
mardi:Q60	Eigen energies of the Hamiltonian	Small (KB - MB)	Matlab vector	console output		Text	No	Yes	42 years
mardi:Q61	testname

Reproducibility

Mathematical Reproducibility

Yes

Runtime Reproducibility

Yes

Reproducibility of Results

Yes

Reproducibility on original Hardware

Yes

Reproducibility on other Hardware

Yes

Transferability to

other Hamiltonians

Legend

The following abbreviations are used in the document to indicate/resolve IDs:

doi: DOI / https://dx.doi.org/

sw: swMATH / https://swmath.org/software/

wikidata: https://www.wikidata.org/wiki/

mardi: https://portal.mardi4nfdi.de/wiki/