Bound states of a Klein-Gordon particle in presence of a smooth potential well

Abstract

We solve the one-dimensional time-independent Klein-Gordon equation in presence of a smooth potential well. The bound state solutions are given in terms of the Whittaker $M_{\kappa ,\mu }(x)$ function, and the antiparticle bound state is discussed in terms of potential parameters.

9 pages, 4 figures. International Journal of Modern Physics A (2020)