A High-Order Integrator for the Schrödinger Equation with Time-Dependent, Homogeneous Magnetic Field

We construct a family of numerical methods for the Pauli equation charged particles in time-dependent, homogeneous magnetic field. These are described general setting comprising systems multiple and extend usual splitting Fourier grid approach. The issue is that field causes to rotate. corresponding rotations wave function highly incompatible with approach used standard Schrödinger equation. Motivated by theory Lie algebras their representations, our new approximates exact flow map terms rotated potentials initial data, thereby avoids this issue. Finally, we provide examples examine convergence preservation norm energy.