Exact Solutions of Relativistic Wave Equations

Duffin–Kemmer–Petiau and Dirac Equations—A Supersymmetric Connection

“…This is the case of longitudinal potentials for which several exact solutions of the Dirac equation were found [10].…”

“…In what follows we shall work with external fields of special configuration, so-called crossed and longitudinal fields, non-standard but Lorentz covariant, see [10]. We shall also need elements of spinor calculus.…”

“…It is possible to separate variables in Equations (33) and (34) following procedures described in [10]. Substituting ξ 1…”

“…where λ 2 1 is the separation constant and we note that Equations (46a) and (46b) are analogous to Equations (12.15) and (12.19) in [10].…”

“…Substituting first two equations into the third one in Equation (61), we get the Klein-Gordon equation π µ π µ ψ = m 2 ψ, which can be solved via separation of variables for the case of crossed fields, see Chapter 3 in [10] (the same can be done in Equation (62)). …”