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Title: Propagator for finite range potentials: The case of reflection

Abstract

Following a previous study on the transmission propagator for a finite range potential, the problem of reflection is considered. It is found that the Laplace transform of the reflection propagator can be expressed in terms of the usual Fredholm determinant {delta} and of a new similar determinant {gamma}, containing the peculiar characteristics of reflection. As an example, an array of delta potentials is considered. Moreover, a possible application to the calculation of quantum traversal time is shown.

Authors:
;  [1];  [2]
  1. Istituto di Fisica Applicata 'Nello Carrara', CNR, via Madonna del Piano 10, 50019 Sesto Fiorentino, Florence (Italy)
  2. (Italy)
Publication Date:
OSTI Identifier:
20929680
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 48; Journal Issue: 4; Other Information: DOI: 10.1063/1.2728518; (c) 2007 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; LAPLACE TRANSFORMATION; POTENTIALS; PROPAGATOR; REFLECTION; SCHROEDINGER EQUATION

Citation Formats

Cacciari, Ilaria, Moretti, Paolo, and Istituto dei Sistemi Complessi, CNR, Sezione di Firenze, via Madonna del Piano 10, Sesto Fiorentino, Florence 50019. Propagator for finite range potentials: The case of reflection. United States: N. p., 2007. Web. doi:10.1063/1.2728518.
Cacciari, Ilaria, Moretti, Paolo, & Istituto dei Sistemi Complessi, CNR, Sezione di Firenze, via Madonna del Piano 10, Sesto Fiorentino, Florence 50019. Propagator for finite range potentials: The case of reflection. United States. doi:10.1063/1.2728518.
Cacciari, Ilaria, Moretti, Paolo, and Istituto dei Sistemi Complessi, CNR, Sezione di Firenze, via Madonna del Piano 10, Sesto Fiorentino, Florence 50019. Sun . "Propagator for finite range potentials: The case of reflection". United States. doi:10.1063/1.2728518.
@article{osti_20929680,
title = {Propagator for finite range potentials: The case of reflection},
author = {Cacciari, Ilaria and Moretti, Paolo and Istituto dei Sistemi Complessi, CNR, Sezione di Firenze, via Madonna del Piano 10, Sesto Fiorentino, Florence 50019},
abstractNote = {Following a previous study on the transmission propagator for a finite range potential, the problem of reflection is considered. It is found that the Laplace transform of the reflection propagator can be expressed in terms of the usual Fredholm determinant {delta} and of a new similar determinant {gamma}, containing the peculiar characteristics of reflection. As an example, an array of delta potentials is considered. Moreover, a possible application to the calculation of quantum traversal time is shown.},
doi = {10.1063/1.2728518},
journal = {Journal of Mathematical Physics},
number = 4,
volume = 48,
place = {United States},
year = {Sun Apr 15 00:00:00 EDT 2007},
month = {Sun Apr 15 00:00:00 EDT 2007}
}