# Propagator for finite range potentials

## Abstract

The Schroedinger equation in integral form is applied to the one-dimensional scattering problem in the case of a general finite range, nonsingular potential. A simple expression for the Laplace transform of the transmission propagator is obtained in terms of the associated Fredholm determinant, by means of matrix methods; the particular form of the kernel and the peculiar aspects of the transmission problem play an important role. The application to an array of delta potentials is shown.

- Authors:

- Istituto di Fisica Applicata 'Nello Carrara', C.N.R., via Madonna del Piano 10, 50019 Sesto Fiorentino, Florence (Italy)
- (Italy)

- Publication Date:

- OSTI Identifier:
- 20861555

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Mathematical Physics; Journal Volume: 47; Journal Issue: 12; Other Information: DOI: 10.1063/1.2401728; (c) 2006 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; ALGEBRA; INTEGRAL EQUATIONS; LAPLACE TRANSFORMATION; ONE-DIMENSIONAL CALCULATIONS; POTENTIAL SCATTERING; POTENTIALS; PROPAGATOR; SCHROEDINGER EQUATION

### Citation Formats

```
Cacciari, Ilaria, Moretti, Paolo, and Istituto dei Sistemi Complessi, C.N.R., Sezione di Firenze, via Madonna del Piano 10, 50019 Sesto Fiorentino, Florence.
```*Propagator for finite range potentials*. United States: N. p., 2006.
Web. doi:10.1063/1.2401728.

```
Cacciari, Ilaria, Moretti, Paolo, & Istituto dei Sistemi Complessi, C.N.R., Sezione di Firenze, via Madonna del Piano 10, 50019 Sesto Fiorentino, Florence.
```*Propagator for finite range potentials*. United States. doi:10.1063/1.2401728.

```
Cacciari, Ilaria, Moretti, Paolo, and Istituto dei Sistemi Complessi, C.N.R., Sezione di Firenze, via Madonna del Piano 10, 50019 Sesto Fiorentino, Florence. Fri .
"Propagator for finite range potentials". United States.
doi:10.1063/1.2401728.
```

```
@article{osti_20861555,
```

title = {Propagator for finite range potentials},

author = {Cacciari, Ilaria and Moretti, Paolo and Istituto dei Sistemi Complessi, C.N.R., Sezione di Firenze, via Madonna del Piano 10, 50019 Sesto Fiorentino, Florence},

abstractNote = {The Schroedinger equation in integral form is applied to the one-dimensional scattering problem in the case of a general finite range, nonsingular potential. A simple expression for the Laplace transform of the transmission propagator is obtained in terms of the associated Fredholm determinant, by means of matrix methods; the particular form of the kernel and the peculiar aspects of the transmission problem play an important role. The application to an array of delta potentials is shown.},

doi = {10.1063/1.2401728},

journal = {Journal of Mathematical Physics},

number = 12,

volume = 47,

place = {United States},

year = {Fri Dec 15 00:00:00 EST 2006},

month = {Fri Dec 15 00:00:00 EST 2006}

}

DOI: 10.1063/1.2401728

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