# Perturbation theory for short-range weakly-attractive potentials in one dimension

## Abstract

We have obtained the perturbative expressions up to sixth order for the energy of the bound state in a one dimensional, arbitrarily weak, short range finite well, applying a method originally developed by Gat and Rosenstein Ref. [1]. The expressions up to fifth order reproduce the results already known in the literature, while the sixth order had not been calculated before. As an illustration of our formulas we have applied them to two exactly solvable problems and to a nontrivial problem.

- Authors:

- Facultad de Ciencias, CUICBAS, Universidad de Colima, Bernal Díaz del Castillo 340, Colima, Colima (Mexico)
- INIFTA (UNLP, CONICET), Division Química Teórica, Blvd. 113 S/N, Sucursal 4, Casilla de Correo 16, 1900 La Plata (Argentina)

- Publication Date:

- OSTI Identifier:
- 22617484

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Annals of Physics; Journal Volume: 378; Other Information: Copyright (c) 2017 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BOUND STATE; EXACT SOLUTIONS; ONE-DIMENSIONAL CALCULATIONS; PERTURBATION THEORY; QUANTUM WELLS

### Citation Formats

```
Amore, Paolo, E-mail: paolo.amore@gmail.com, and Fernández, Francisco M., E-mail: fernande@quimica.unlp.edu.ar.
```*Perturbation theory for short-range weakly-attractive potentials in one dimension*. United States: N. p., 2017.
Web. doi:10.1016/J.AOP.2017.01.022.

```
Amore, Paolo, E-mail: paolo.amore@gmail.com, & Fernández, Francisco M., E-mail: fernande@quimica.unlp.edu.ar.
```*Perturbation theory for short-range weakly-attractive potentials in one dimension*. United States. doi:10.1016/J.AOP.2017.01.022.

```
Amore, Paolo, E-mail: paolo.amore@gmail.com, and Fernández, Francisco M., E-mail: fernande@quimica.unlp.edu.ar. Wed .
"Perturbation theory for short-range weakly-attractive potentials in one dimension". United States.
doi:10.1016/J.AOP.2017.01.022.
```

```
@article{osti_22617484,
```

title = {Perturbation theory for short-range weakly-attractive potentials in one dimension},

author = {Amore, Paolo, E-mail: paolo.amore@gmail.com and Fernández, Francisco M., E-mail: fernande@quimica.unlp.edu.ar},

abstractNote = {We have obtained the perturbative expressions up to sixth order for the energy of the bound state in a one dimensional, arbitrarily weak, short range finite well, applying a method originally developed by Gat and Rosenstein Ref. [1]. The expressions up to fifth order reproduce the results already known in the literature, while the sixth order had not been calculated before. As an illustration of our formulas we have applied them to two exactly solvable problems and to a nontrivial problem.},

doi = {10.1016/J.AOP.2017.01.022},

journal = {Annals of Physics},

number = ,

volume = 378,

place = {United States},

year = {Wed Mar 15 00:00:00 EDT 2017},

month = {Wed Mar 15 00:00:00 EDT 2017}

}

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