TY - UNPB
T1 - A time splitting method for the three-dimensional linear Pauli equation
AU - Gutleb, Timon S.
AU - Mauser, Norbert J.
AU - Ruggeri, Michele
AU - Stimming, Hans-Peter
PY - 2020/5/12
Y1 - 2020/5/12
N2 - We present and 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, the latter missing in predeeding work on the linear magnetic Schrödinger equation. We use a four 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 (= "linear" case), thus providing a generalization of previous results for the magnetic Schrödinger equation. Some proof of concept examples of numerical simulations are presented.
AB - We present and 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, the latter missing in predeeding work on the linear magnetic Schrödinger equation. We use a four 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 (= "linear" case), thus providing a generalization of previous results for the magnetic Schrödinger equation. Some proof of concept examples of numerical simulations are presented.
KW - Pauli equation
KW - operator splitting
KW - time splitting
KW - magnetic Schrödinger equation
KW - semi-relativistic quantum mechanics
U2 - 10.48550/arXiv.2005.06072
DO - 10.48550/arXiv.2005.06072
M3 - Working Paper/Preprint
BT - A time splitting method for the three-dimensional linear Pauli equation
CY - Ithaca, N.Y.
ER -