Time-dependent step-like potential with a freezable bound state in the continuum

Izamar Gutiérrez Altamirano, Alonso Contreras-Astorga, Alfredo Raya Montaño

Time-dependent step-like potential with a freezable bound state in the continuum

Číslo: 1/2022
Periodikum: Acta Polytechnica
DOI: 10.14311/AP.2022.62.0056

Klíčová slova: bound states in the continuum, supersymmetric quantum mechanics, time-dependent quantum systems

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Anotace: In this work, we construct a time-dependent step-like potential supporting a normalizable state with energy embedded in the continuum. The potential is allowed to evolve until a stopping time ti, where it becomes static. The normalizable state also evolves but remains localized at every fixed time up to ti. After this time, the probability density of this state freezes becoming a Bound state In the Continuum. Closed expressions for the potential, the freezable bound state in the continuum, and scattering states are given.