With the aid of factorization of the Schrödinger operator by quaternionic differential operators of first order proposed in recent works by S. Bernstein and K. Gürlebeck we study the system describing forcefree magnetic fields with nonconstant proportionality factor, the static Maxwell system for inhomogeneous media, the Beltrami condition and the Dirac equation with different types of potentials depending on one variable. We obtain integral representations for solutions of these systems.
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