View source for Numerical quantum dynamics using WavePacket

PID (if applicable): No

<span id="problem-statement"></span>
== Problem Statement ==

Solve Schrödingers equations

<span id="object-of-research-and-objective"></span>
=== Object of Research and Objective ===

Solve Schrödingers equations

<span id="procedure"></span>
=== 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.

<span id="involved-disciplines"></span>
=== Involved Disciplines ===

<b>Mathematical Areas:</b>

1 - [https://staging.mardi4nfdi.org/wiki/Item:Q63 partial differential equation]<br/> 2 - [https://staging.mardi4nfdi.org/wiki/Item:Q64 Schrödinger equation]

<b>Non-Mathematical Disciplines:</b>

1 - [https://staging.mardi4nfdi.org/wiki/Item:Q62 quantum mechanics]

<span id="data-streams"></span>
=== Data Streams ===

wave functions

<span id="model"></span>
== Model ==

ID: mardi:[https://staging.mardi4nfdi.org/wiki/Item:Q56 Q56]

time-independent Schrödinger equation

eigenvalue equation for the Hamiltonian operator

<span id="discretization"></span>
=== Discretization ===

* Time:
* Space: Fourier/Plane wave

<span id="variables"></span>
=== Variables ===

{| class="wikitable" class="wikitable"
|-
! Name
! Unit
! Symbol
|-
| Energy
| J
| E
|-
| Hamiltonian
| J
| <math display="inline">\hat{H}</math>
|-
| Quantum Number
| dimensionsless
| n
|-
| Quantum State
| <math display="inline">1/\sqrt(length)</math>
| <math display="inline">\psi</math>
|}

<span id="parameters"></span>
=== Parameters ===

{| class="wikitable" class="wikitable"
|-
! Name
! Unit
! Symbol
|-
|
|
|
|}

<span id="process-information"></span>
== Process Information ==

<span id="process-steps"></span>
=== Process Steps ===

{| class="wikitable" class="wikitable"
|-
! Name
! Description
! Input
! Output
! Method
! Parameter
! Environment
! Mathematical Area
|-
|
|
|
|
|
|
|
|
|}

<span id="applied-methods"></span>
=== Applied Methods ===

{| class="wikitable" class="wikitable"
|-
! ID
! Name
! Process Step
! Parameter
! implemented by
|-
| mardi:[https://staging.mardi4nfdi.org/wiki/Item:Q57 Q57]
| diagonalization
|
|
| WavePacket
|}

<span id="software-used"></span>
=== Software used ===

{| class="wikitable" class="wikitable"
|-
! ID
! Name
! Description
! Version
! Programming Language
! Dependencies
! versioned
! published
! documented
|-
| mardi:[https://staging.mardi4nfdi.org/wiki/Item:Q59 Q59]
| WavePacket
| Numerical Quantum Dynamics
| 7.2.1
| [https://staging.mardi4nfdi.org/wiki/Item:Q58 MatLab]<br/>
|
| Yes
| [https://sourceforge.net/projects/wavepacket/ Yes]
| [https://sourceforge.net/p/wavepacket/wiki/Home/ Yes]
|}

<span id="hardware"></span>
=== Hardware ===

{| class="wikitable" class="wikitable"
|-
! ID
! Name
! Processor
! Compiler
! #Nodes
! #Cores
|-
|
|
|
|
|
|
|}

<span id="input-data"></span>
=== Input Data ===

{| class="wikitable" class="wikitable"
|-
! ID
! Name
! Size
! Data Structure
! Format Representation
! Format Exchange
! binary/text
! proprietary
! to publish
! to archive
|-
|
|
|
|
|
|
|
|
|
|
|}

<span id="output-data"></span>
=== Output Data ===

{| class="wikitable" class="wikitable"
|-
! ID
! Name
! Size
! Data Structure
! Format Representation
! Format Exchange
! binary/text
! proprietary
! to publish
! to archive
|-
| mardi:[https://staging.mardi4nfdi.org/wiki/Item:Q60 Q60]
| Eigen energies of the Hamiltonian
| Small (KB - MB)
| Matlab vector
| console output
|
| Text
| No
| Yes
| 42 years
|-
| mardi:[https://staging.mardi4nfdi.org/wiki/Item:Q61 Q61]
| testname
|
|
|
|
|
|
|
|
|}

<span id="reproducibility"></span>
== Reproducibility ==

<span id="mathematical-reproducibility"></span>
=== Mathematical Reproducibility ===

Yes

<span id="runtime-reproducibility"></span>
=== Runtime Reproducibility ===

Yes

<span id="reproducibility-of-results"></span>
=== Reproducibility of Results ===

Yes

<span id="reproducibility-on-original-hardware"></span>
=== Reproducibility on original Hardware ===

Yes

<span id="reproducibility-on-other-hardware"></span>
=== Reproducibility on other Hardware ===

Yes

<span id="transferability-to"></span>
=== Transferability to ===

other Hamiltonians

<span id="legend"></span>
== 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/