Reflectionless potentials for the one-dimensional Dirac equation: Pseudoscalar potentials

For the Dirac equation in one dimension, a method for constructing reflectionless pseudoscalar potentials is presented. This is a relativistic generalization of Kay and Moses’s classic method [J. Appl. Phys. 27, 1503 (1956)] that deals with a similar problem for the Schrödinger equation. This can also be viewed as an inverse scattering problem. For a set of assumed energy levels, the method furnishes a family of potentials, each of which reproduces the energy levels. These potentials are all reflectionless.