# Semiclassical model of a one-dimensional quantum dot

## Abstract

A one-dimensional quantum dot at zero temperature is used as an example for developing a consistent semiclassical method. The method can also be applied to systems of higher dimension that admit separation of variables. For electrons confined by a quartic potential, the Thomas-Fermi approximation is used to calculate the self-consistent potential, the electron density distribution, and the total energy as a function of the electron number and the effective electron charge representing the strength of interaction between electrons. Use is made of scaling with respect to the electron number. An energy quantization condition is derived. The oscillating part of the electron density and both gradient and shell corrections to the total electron energy are calculated by using the results based on the Thomas-Fermi model and analytical expressions derived in this study. The dependence of the shell correction on the interaction strength is examined. Comparisons with results calculated by the density functional method are presented. The relationship between the results obtained and the Strutinsky correction is discussed.

- Authors:

- Russian Academy of Sciences, Institute of Mathematical Modeling (Russian Federation), E-mail: shpat@imamod.ru

- Publication Date:

- OSTI Identifier:
- 21067722

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Experimental and Theoretical Physics; Journal Volume: 102; Journal Issue: 3; Other Information: DOI: 10.1134/S1063776106030095; Copyright (c) 2006 Nauka/Interperiodica; Article Copyright (c) 2006 Pleiades Publishing, Inc; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CORRECTIONS; DENSITY FUNCTIONAL METHOD; ELECTRON DENSITY; ELECTRONS; FUNCTIONS; INTERACTIONS; ONE-DIMENSIONAL CALCULATIONS; POTENTIALS; QUANTIZATION; QUANTUM DOTS; SEMICLASSICAL APPROXIMATION; THOMAS-FERMI MODEL

### Citation Formats

```
Shpatakovskaya, G. V.
```*Semiclassical model of a one-dimensional quantum dot*. United States: N. p., 2006.
Web. doi:10.1134/S1063776106030095.

```
Shpatakovskaya, G. V.
```*Semiclassical model of a one-dimensional quantum dot*. United States. doi:10.1134/S1063776106030095.

```
Shpatakovskaya, G. V. Wed .
"Semiclassical model of a one-dimensional quantum dot". United States.
doi:10.1134/S1063776106030095.
```

```
@article{osti_21067722,
```

title = {Semiclassical model of a one-dimensional quantum dot},

author = {Shpatakovskaya, G. V.},

abstractNote = {A one-dimensional quantum dot at zero temperature is used as an example for developing a consistent semiclassical method. The method can also be applied to systems of higher dimension that admit separation of variables. For electrons confined by a quartic potential, the Thomas-Fermi approximation is used to calculate the self-consistent potential, the electron density distribution, and the total energy as a function of the electron number and the effective electron charge representing the strength of interaction between electrons. Use is made of scaling with respect to the electron number. An energy quantization condition is derived. The oscillating part of the electron density and both gradient and shell corrections to the total electron energy are calculated by using the results based on the Thomas-Fermi model and analytical expressions derived in this study. The dependence of the shell correction on the interaction strength is examined. Comparisons with results calculated by the density functional method are presented. The relationship between the results obtained and the Strutinsky correction is discussed.},

doi = {10.1134/S1063776106030095},

journal = {Journal of Experimental and Theoretical Physics},

number = 3,

volume = 102,

place = {United States},

year = {Wed Mar 15 00:00:00 EST 2006},

month = {Wed Mar 15 00:00:00 EST 2006}

}