Exact energy eigenvalues of the generalized Dirac-Coulomb equation via a modified similarity transformation

TL;DR

This paper derives exact energy eigenvalues for a generalized Dirac-Coulomb system using a modified similarity transformation, simplifying the equations to relate to the Schrödinger equation solutions.

Contribution

It introduces a modified similarity transformation that enables exact solutions for the generalized Dirac-Coulomb equation with specific potentials.

Findings

Exact energy eigenvalues obtained for the generalized Dirac-Coulomb system.

Transformed radial equations resemble Schrödinger equation solutions.

Simplification facilitates analytical solutions for complex relativistic potentials.

Abstract

With the aid of a modified similarity transformation we obtained exact energy eigenvalues of the generalized Dirac-Coulomb equation. This equation consists of the time component of the Lorentz 4-vector potential V_v(r)=-A_1/r, and a Lorentz scalar potential V_s(r)=-A_2/r. The transformed radial equations are so simple that their solutions are inferred from the conventional solutions of the Schrodinger equation.