# 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:

- Istituto di Fisica Applicata 'Nello Carrara', CNR, via Madonna del Piano 10, 50019 Sesto Fiorentino, Florence (Italy)
- (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}

}

DOI: 10.1063/1.2728518

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