Resonant states in an attractive one dimensional cusp potential

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.

11 pages. To appear in Physica Scripta

References in corpus (7)

• The Woods-Saxon Potential in the Dirac Equation
• Supercriticality and Transmission Resonances in the Dirac equation
• Transmission resonances and supercritical states in a one dimensional cusp potential
• Low Momentum Scattering in the Dirac Equation
• Levinson theorem for Dirac particles in one dimension
• The Strong Levinson Theorem for the Dirac Equation
• Phase shifts and resonances in the Dirac equation

Cited by in corpus (7)

• Bound states of the Duffin-Kemmer-Petiau equation with a mixed minimal-nonminimal vector cusp potential
• Scattering, bound and quasi-bound states of the generalized symmetric Woods-Saxon potential
• Relativistic Stark resonances in a simple exactly soluble model for a diatomic molecule
• Tunneling and transmission resonances of a Dirac particle by a double barrier
• Particle resonance in the Dirac equation in the presence of a delta interaction and a perturbative hyperbolic potential
• Scattering of a Klein-Gordon particle by a smooth barrier
• Full transmission within a wide energy range and super-criticality in relativistic barrier scattering