Bound states of scalar particles in the presence of a short range potential

TL;DR

This paper investigates the energy spectrum of scalar particles described by the Klein-Gordon equation within a short-range truncated hyperbolic tangent potential, revealing the possibility of bound states embedding into the negative energy continuum and exhibiting resonant behavior.

Contribution

It demonstrates that relativistic scalar particles in one-dimensional short-range potentials can show resonant states, challenging the common belief that only the Schiff-Snyder effect occurs.

Findings

Bound states can embed into the negative energy continuum.

Resonant behavior can occur in relativistic scalar particles.

Contradicts the common belief of only Schiff-Snyder effect in such systems.

Abstract

We analyze the behavior of the energy spectrum of the Klein-Gordon equation in the presence of a truncated hyperbolic tangent potential. From our analysis we obtain that, for some values of the potential there is embedding of the bound states into the negative energy continuum, showing that, in opposition to the general belief, relativistic scalar particles in one-dimensional short range potentials can exhibit resonant behavior and not only the Schiff-Snyder effect.