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Scattering of a relativistic scalar particle by a cusp potential

2006; Elsevier BV; Volume: 362; Issue: 1 Linguagem: Inglês

10.1016/j.physleta.2006.09.089

1873-2429

Vı́ctor M. Villalba, Clara Rojas,

Quantum chaos and dynamical systems

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.