Abstract
We analyze a numerical method to solve the time-dependent linear Pauli equation in three space dimensions. The Pauli equation is a semi-relativistic generalization of the Schrödinger equation for 2-spinors which accounts both for magnetic fields and for spin, with the latter missing in preceding numerical work on the linear magnetic Schrödinger equation. We use a four term operator splitting in time, prove stability and convergence of the method and derive error estimates as well as meshing strategies for the case of given time-independent electromagnetic potentials, thus providing a generalization of previous results for the magnetic Schrödinger equation.
| Translated title of the contribution | Eine Time-Splitting-Methode fuer die dreidimensionale lineare Pauli-Gleichung |
|---|---|
| Original language | English |
| Pages (from-to) | 399-412 |
| Number of pages | 14 |
| Journal | Computational Methods in Applied Mathematics |
| Volume | 24 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 1 Apr 2024 |
Austrian Fields of Science 2012
- 101014 Numerical mathematics
Keywords
- Pauli Equation
- Operator Splitting
- Time Splitting
- Magnetic Schrödinger Equation
- Semi-Relativistic Quantum Mechanics
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