Bound states of a Klein–Gordon particle in the presence of a smooth potential well
Bound states of a Klein–Gordon particle in the presence of a smooth potential well
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.