We discuss hierarchies of PDE models in relativistic quantum mechanics, from the fully relativistic Dirac and Klein-Gordon equation to the non-relativistic Schrodinger equation.  The Pauli equation is the first order (in 1/c, where c is the speed of light) correction of the Schrodinger 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.

Prof. Dr. Norbert Mauser is the director of Wolfgang Pauli Institute and professor at University of Vienna. He received Ph.D from TU Vienna in 1994. In 2001, together with Peter Markowich, he founded the Wolfgang Pauli Institute, of which he has been director ever since. Prof. Mauser has leaded many research projects including EU research training network "HYperbolic and Kinetic Equations : Asymptotics, Numerics, Applications" and EU Marie Curie Early Stage Training multi Site "Differential Equations and Applications in Science and Engineering".  His research interests are focused on partial differential equations: (asymptotic) analysis, modeling, numerics & simulations, generalized nonlinear Schrödinger equations (NLS), applications in quantum physics.