Separation of variables and exact solution of the Klein–Gordon and Dirac equations in an open universe

Abstract

We solve the Klein-Gordon and Dirac equations in an open cosmological universe with a partially horn topology in the presence of a time dependent magnetic field. Since the exact solution cannot be obtained explicitly for arbitrary time-dependence of the field, we discuss the asymptotic behavior of the solutions with the help of the relativistic Hamilton-Jacobi equation.

A Square-Integrable Spinor Solution to Non-Interacting Dirac Equations

“…One of the most important problems in mathematical physics is to study the properties of the Dirac spinor field equations by assigning a specific potential and finding its exact solutions, according to various methods [1][2][3][4][5][6][7][8][9][10][11][12][13].…”

Angular-Radial Integrability of Coulomb-like Potentials in Dirac Equations

“…And for it, the Coulomb potential is certainly the simplest. Still, the problem of finding exact solutions is always treated in ways that strongly depend on variable separation [1][2][3][4][5][6][7][8], and more in general on various assumptions that tend to limit the range of validity of the method. Meaning, the method used to find solutions with separation of variables for the Coulomb potential can hardly be used to find solutions with no separability of the variables for more general potentials.…”

Exact Solution of the Curved Dirac Equation in Polar Coordinates: Master Function Approach

“…The Dirac equation in curved space-time has been considered in different curved backgrounds due to its considerable applications in astrophysics, cosmology, and condensed matter [6][7][8][9]. On the other hand, in recent years, different methods have been applied in order to study the Dirac equation such as separation of variables [10,11], supersymmetric quantum mechanics [12,13], and Nikiforov-Uvarov [14,15]. As we know the supersymmetry [16] and shape invariance [17] formalism is one of the most important methods which has been successfully used in order to study exactly solvable quantum systems.…”