A time splitting method for the three-dimensional linear Pauli equation

Timon S. Gutleb, Norbert J. Mauser, Michele Ruggeri, Hans Peter Stimming

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1 Citation (Scopus)
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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.
Original languageEnglish
Pages (from-to)407-420
Number of pages14
JournalComputational Methods in Applied Mathematics
Issue number2
Early online date6 Oct 2023
Publication statusPublished - 1 Apr 2024


  • Pauli equation
  • operator splitting
  • time splitting
  • magnetic Schrödinger equation
  • semi-relativistic quantum mechanics


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