Numerical quantum dynamics using WavePacket 1
PID (if applicable): No
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:
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
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/
