# Properties of a finite fully spin-polarized free homogeneous one-dimensional electron gas

## Abstract

The homogeneous electron gas model has been quite successful to predict the bulk properties of systems of electrons at various densities. In many occasions, a simplified free homogeneous electron gas model represents a powerful first approximation to a real system. Despite our considerable knowledge on the bulk properties of a homogeneous electron gas, advances in nanoscience and nanotechnology call for a greater effort to understand the opposite limit of small finite systems of electrons with size-dependent properties. In this work, we provide a detailed description of the properties of a finite fully spin-polarized (spinless) free homogeneous one-dimensional electron gas, the simplest of the free homogeneous electron gases. We derive exact analytical results for various quantities such as the one-particle density function, two-particle density function, one-particle density matrix, pair correlation function and energy of finite systems with an arbitrary number of electrons. The results obtained provide a detailed view on how various quantities corresponding to a finite system approach their bulk (thermodynamic limit) value.

- Authors:

- Department of Physics, Prairie View A and M University, Prairie View, Texas 77446 (United States)

- Publication Date:

- OSTI Identifier:
- 22454438

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: AIP Advances; Journal Volume: 5; Journal Issue: 1; Other Information: (c) 2015 Author(s); Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 36 MATERIALS SCIENCE; 77 NANOSCIENCE AND NANOTECHNOLOGY; DENSITY; DENSITY MATRIX; ELECTRON GAS; ELECTRONS; NANOSTRUCTURES; NANOTECHNOLOGY; PARTICLES; SPIN ORIENTATION

### Citation Formats

```
Ciftja, Orion.
```*Properties of a finite fully spin-polarized free homogeneous one-dimensional electron gas*. United States: N. p., 2015.
Web. doi:10.1063/1.4907104.

```
Ciftja, Orion.
```*Properties of a finite fully spin-polarized free homogeneous one-dimensional electron gas*. United States. doi:10.1063/1.4907104.

```
Ciftja, Orion. Thu .
"Properties of a finite fully spin-polarized free homogeneous one-dimensional electron gas". United States.
doi:10.1063/1.4907104.
```

```
@article{osti_22454438,
```

title = {Properties of a finite fully spin-polarized free homogeneous one-dimensional electron gas},

author = {Ciftja, Orion},

abstractNote = {The homogeneous electron gas model has been quite successful to predict the bulk properties of systems of electrons at various densities. In many occasions, a simplified free homogeneous electron gas model represents a powerful first approximation to a real system. Despite our considerable knowledge on the bulk properties of a homogeneous electron gas, advances in nanoscience and nanotechnology call for a greater effort to understand the opposite limit of small finite systems of electrons with size-dependent properties. In this work, we provide a detailed description of the properties of a finite fully spin-polarized (spinless) free homogeneous one-dimensional electron gas, the simplest of the free homogeneous electron gases. We derive exact analytical results for various quantities such as the one-particle density function, two-particle density function, one-particle density matrix, pair correlation function and energy of finite systems with an arbitrary number of electrons. The results obtained provide a detailed view on how various quantities corresponding to a finite system approach their bulk (thermodynamic limit) value.},

doi = {10.1063/1.4907104},

journal = {AIP Advances},

number = 1,

volume = 5,

place = {United States},

year = {Thu Jan 15 00:00:00 EST 2015},

month = {Thu Jan 15 00:00:00 EST 2015}

}