Numerical quantum dynamics using WavePacket 4

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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
Quantum Number dimensionsless n
Quantum State

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

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