Quaternionic factorization of the Schroedinger operator and its applications to some first order systems of mathematical physics

Abstract

We consider the following first order systems of mathematical physics. 1.The Dirac equation with scalar potential. 2.The Dirac equation with electric potential. 3.The Dirac equation with pseudoscalar potential. 4.The system describing non-linear force free magnetic fields or Beltrami fields with nonconstant proportionality factor. 5.The Maxwell equations for slowly changing media. 6.The static Maxwell system. We show that all this variety of first order systems reduces to a single quaternionic equation the analysis of which in its turn reduces to the solution of a Schroedinger equation with biquaternionic potential. In some important situations the biquaternionic potential can be diagonalized and converted into scalar potentials.

References in corpus (1)

• Force Free Configurations of Vortices in High Temperature Superconductors near H_{c2}

Cited by in corpus (6)

• On a quaternionic Maxwell equation for the time-dependent electromagnetic field in a chiral medium
• Dirac solutions for quaternionic potentials
• On the reduction of the multidimensional Schroedinger equation to a first order equation and its relation to the pseudoanalytic function theory
• Numerical Clifford Analysis for Nonlinear Schrodinger Problem
• Quaternions in mathematical physics (1): Alphabetical bibliography
• On a complex differential Riccati equation