2006/10/07 by Victor M. Villalba, Vı́ctor M. Villalba, Clara Rojas · 1 citation
Physics and Astronomy · #Bound state #Cold Atom Physics and Bose-Einstein Condensates #Cusp (singularity) #Klein–Gordon equation #Limit (mathematics) #Mathematical analysis #Mathematical physics #Momentum (technical analysis) #Physics #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Quantum electrodynamics #Quantum mechanics #Reflection (computer programming) #Scalar (mathematics) #Scattering #hep-th #quant-ph
paper · pdf · doi:10.1016/j.physleta.2006.09.089
published as Phys.Lett.A362:21-25,2007 · To appear in Physics Letters A
arxiv created 2006/10/07 · openalex publication_date 2006/10/07 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.