Nonlocal separable potential in the one-dimensional Dirac equation

The one-dimensional Dirac equation is solved for a separable potential of the form of Lorentz scalar plus vector, (βg+h)v(x)v(x’). Exact analytic solutions are obtained for bound and scattering states for arbitrary v(x). For a particular combination of the values of g and h, degeneracy of the bound state occurs, and total reflection also takes place for a certain incident energy. The limiting case, in which v(x) becomes a delta function, is discussed in detail.