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Complex Form of Classical and Quantum Electrodynamics
Sergey I. Kryuchkov, Nathan A. Lanfear, Sergei K. Suslov
We consider a complex covariant form of the macroscopic Maxwell equations, in a moving medium or at rest, following the original ideas of Minkowski. A compact, Lorentz invariant, d…
The Role of the Pauli-Lubanski Vector for the Dirac, Weyl, Proca, Maxwell, and Fierz-Pauli Equations
Sergey I. Kryuchkov, Nathan A. Lanfear, Sergei K. Suslov
We analyze basic relativistic wave equations for the classical fields, such as Dirac's equation, Weyl's two-component equation for massless neutrinos, and the Proca, Maxwell, and F…
Exact Wave Functions for Generalized Harmonic Oscillators
Nathan Lanfear, Raquel M. Lopez, Sergei K. Suslov
We transform the time-dependent Schroedinger equation for the most general variable quadratic Hamiltonians into a standard autonomous form. As a result, the time-evolution of exact…
The time-dependent Schroedinger equation, Riccati equation and Airy functions
Nathan Lanfear, Sergei K. Suslov
We construct the Green functions (or Feynman's propagators) for the Schroedinger equations of the form in terms of Airy functions and solve the Ca…