Scattering of a relativistic scalar particle by a cusp potential

Abstract

We solve the Klein-Gordon equation in the presence of a spatially one-dimensional cusp potential. The scattering solutions are obtained in terms of Whittaker functions and the condition for the existence of transmission resonances is derived. We show the dependence of the zero-reflection condition on the shape of the potential. In the low momentum limit, transmission resonances are associated with half-bound states. We express the condition for transmission resonances in terms of the phase shifts.

arXiv commentTo appear in Physics Letters A

References in corpus (6)

• The Woods-Saxon Potential in the Dirac Equation
• Scattering of a Klein-Gordon particle by a Woods-Saxon potential
• Supercriticality and Transmission Resonances in the Dirac equation
• Bound states of the Klein-Gordon equation in the presence of short-range potentials
• Transmission resonances and supercritical states in a one dimensional cusp potential
• Phase shifts and resonances in the Dirac equation

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• Scattering of a scalar relativistic particle by the hyperbolic tangent potential