Total Absorption in Finite Time in an $i\delta$ Potential
Quantum Physics
2007-05-23 v1
Abstract
We consider the evolution of Green's function of the one-dimensional Schr\"odinger equation in the presence of the complex potential . 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.
Cite
@article{arxiv.quant-ph/0107152,
title = {Total Absorption in Finite Time in an $i\delta$ Potential},
author = {A. Marchewka and Zeev Schuss},
journal= {arXiv preprint arXiv:quant-ph/0107152},
year = {2007}
}
Comments
8 pages, no figures, we would welcome comments