Separation of variables in Hamilton–Jacobi and Klein–Gordon–Fock equations for a charged test particle in the stackel spaces of type (1.1)

Abstract

All equivalence classes for electromagnetic potentials and space-time metrics of Stackel spaces provided that Hamilton–Jacobi equation and Klein–Gordon–Fock equation for a charged test particle can be integrated by the method of complete separation of variables are found. The separation is carried out using the complete sets of mutually commuting integrals of motion of type (1.1) whereby in a privileged coordinate system, the given equations turn into parabolic type equations. Hence, these metrics can be used as models for describing plane gravitational waves.