Analytical approximation to the solution of the Dirac equation with the Eckart potential including the spin–orbit coupling term

Abstract

By using the supersymmetric WKB approximation approach and the functional analysis method, we solve approximately the Dirac equation with the Eckart potential for the arbitrary spin–orbit quantum number κ. The bound state energy eigenvalues and the associated two-component spinors of the Dirac particles are obtained approximately.