Resonant states in an attractive one-dimensional cusp potential

Abstract

Abstract. We solve the two-component Dirac equation in the presence of a spatially one dimensional symmetric attractive cusp potential. The components of the spinor solution are expressed in terms of Whittaker functions. We compute the bound states solutions and show that, as the potential amplitude increases, the lowest energy state sinks into the Dirac sea becoming a resonance. We characterize and compute the lifetime of the resonant state with the help of the phase shift and the Breit-Wigner relation. We discuss the limit when the cusp potential reduces to a delta point interaction.

Tunneling and transmission resonances of a Dirac particle by a double barrier

“…The relation between low momentum resonances and supercriticality has been established by Dombey et al [2,10]. Recently [9,10,11], some results on scattering of Dirac particles by one a dimensional potential exhibiting resonant behavior have been reported.…”

“…Using the representation (1), the Dirac equation in the presence of a potential V (x) takes the form [11] […”

Scattering of a Klein–Gordon particle by a smooth barrier

“…This equation have been widely study in the literature for different physical systems both time-independent [1,2,3,4,5,6,7,8,9,10,11,12,13] and timedependent [14,15,16,17] Klein-Gordon equation. The analytical solution of the time-independent Klein-Gordon equation for different potentials has been caused of a lot of interest in recent years, for both bound states [2,3,6,9,12] and scattering solutions [1,4,5,7,8,9,10,11,13]. It has allowed the understanding of several physical phenomena of Relativistic Quantum Mechanics such as the antiparticle bound state [18,19], transmission resonances [1,4,5], and superradiance [20,7,21,22].…”

Relativistic Stark resonances in a simple exactly soluble model for a diatomic molecule

“…In our study, a similar approach is used to study the latter in the relativistic regime using the extension of the WTK method to the Dirac equation [33]. This methodology has been used in [34][35][36][37] to study various potentials, while the atomic case with a single delta function potential was treated in [38].…”