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Total Absorption in Finite Time in an $iδ$ Potential

A. Marchewka·Zeev Schuss
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Abstract

We consider the evolution of Green's function of the one-dimensional Schrödinger equation in the presence of the complex potential $-ikδ(x)$. Our result is the construction of an explicit time-dependent solution which we use to calculate the time-dependent survival probability of a quantum particle. The survival probability decays to zero in finite time, which means that the complex delta potential well is a total absorber for quantum particles. This potential can be interpreted as a killing measure with infinite killing rate concentrated at the origin.

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A. Marchewka, Zeev Schuss. 2001-07-30. Total Absorption in Finite Time in an $iδ$ Potential. https://arxiv.org/abs/quant-ph/0107152

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