A quantum decay model with exact explicit analytical solution

Abstract

A simple decay model is introduced. The model comprises of a point potential well, which experiences an abrupt change. Due to the temporal variation the initial quantum state can either escape from the well or stay localized as a new bound state. The model allows for an exact analytical solution while having the necessary features of a decay process. The results show that the decay is never exponential, as classical dynamics predicts. Moreover, at short times the decay has a \textit{fractional} power law, which differs from perturbation quantum methods predictions.

4 pages, 3 figures

References in corpus (1)

• Generic Short-Time Propagation of Sharp-Boundaries Wave Packets

Cited by in corpus (2)

• Timescales of tunneling decay of a localized state
• Bound Eigenstate dynamics under a sudden shift of the well's wall