English

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 ikδ(x)-ik\delta(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.

Keywords

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

R2 v1 2026-07-22T19:31:53.091Z