TY  - CHAP
A1  - Kravchenko, Viktor
A1  - Kravchenko, Vladislav
T1  - On the Factorization of the Schrödinger Operator and Its Applications for Studying Some First Order Systems of Mathematical Physics
N2  - 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.
KW  - Mathematische Physik
KW  - Faktor <Algebra>
KW  - Hamilton-Operator
KW  - Quaternion
KW  - Differentialoperator
Y1  - 2003
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20111215-3251
ER  - 
TY  - CHAP
A1  - Kravchenko, Vladislav
A1  - Ramirez, Marco P.
T1  - On a purely real quaternionic reformulation of Dirac equation, and some of its relations with Maxwell's equations
N2  - We show a transformation K which allows us to rewrite the Dirac equation in its covariant form in a purely real quaternionic equation. We discuss how this transformation allows us for obtaining a involutive symmetry of the Dirac equation, as well as one simplification of the traditional vector of currents of the Dirac equation in traditional form. We also show the corresponding quaternionic equation for the problem of charge conjugation in the hole theory, and the quaternionic equation of conservation of currents. Finally, we discuss one decomposition of the quaternionic Dirac operator in two Maxwell's operators corresponding to time-harmonic case in homogeneous media, without sources which surprisingly agrees with the well known relation in quantum mechanics between the frequency ù and the impulse p E=p²c²+m²c, where E denotes the energy.
KW  - Dirac-Gleichung
KW  - Transformation
KW  - Quaternion
Y1  - 2003
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20111215-3269
ER  -