Excited State and Product Wavefunctions for the One Dimensional Dirac Equations

In a previous note, the nonrelativistic bound state wavefunction W(x) was written as Wo(x)W1(x) with Wo(x) being the ground state wavefunction. W1(x) satisfies an eigenvalue equation, similar to the Schrodinger equation, but with the potential term replaced with a coupling term: 

-1/2m d/dx d/dx W1(x) - 1/m d/dx W1(x) [ d/dx Wo(x)/Wo(x) ] = (E-Eo) W1 (x)    ((1))

Mathematically, ((1)) may be compared to the hypergeometric differential equation and solutions found for the Schrodinger if coefficients meet certain criteria.  A similar approach applies to the Klein Gordon and Dirac equations In this note, we wish to examine possible physical significance of Wo(x)W1(x). In addition, we wish to obtain an equation, analogous to ((1)) for  both the Klein Gordon and Dirac equations to compare the coupling terms.