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Gutleb, T. S., Mauser, N., Ruggeri, M., & Stimming, H. P. (2019). Computational semi-relativistic quantum mechanics: the Pauli equation. CSRC seminar, Beijing, China. http://hdl.handle.net/20.500.12708/122827
We discuss hierarchies of PDE models in relativistic quantum mechanics, from the fully relativistic Dirac and Klein-Gordon equation to the non-relativistic Schroedinger equation. The Pauli equation is the first order (in 1/c, where c is the speed of light) correction of the Schroedinger equation that includes magnetic fields and spin. We present the equation and it's self-consistent coupling to a first order approximation of the Maxwell equations, yielding the nonlinear Pauli-Poisswell system as first introduced by N. Masmoudi and N.J.M. We adopt the numerical schemes for the magnetic Schrodinger equation based on time splitting, as first introduced by S. Jin and Z. Zhou.
