dorsal/arxiv
View SchemaTotal Absorption in Finite Time in an $i\delta$ Potential
| Authors | A. Marchewka, Zeev Schuss |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0107152 |
| URL | https://arxiv.org/abs/quant-ph/0107152 |
Abstract
We consider the evolution of Green's function of the one-dimensional Schr\"odinger equation in the presence of the complex potential $-ik\delta(x)$. 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.
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"abstract": "We consider the evolution of Green\u0027s function of the one-dimensional\nSchr\\\"odinger equation in the presence of the complex potential $-ik\\delta(x)$.\nOur result is the construction of an explicit time-dependent solution which we\nuse to calculate the time-dependent survival probability of a quantum particle.\nThe survival probability decays to zero in finite time, which means that the\ncomplex delta potential well is a total absorber for quantum particles. This\npotential can be interpreted as a killing measure with infinite killing rate\nconcentrated at the origin.",
"arxiv_id": "quant-ph/0107152",
"authors": [
"A. Marchewka",
"Zeev Schuss"
],
"categories": [
"quant-ph"
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"title": "Total Absorption in Finite Time in an $i\\delta$ Potential",
"url": "https://arxiv.org/abs/quant-ph/0107152"
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