### Abstract

It is known experimentally that stable few-body clusters containing negatively-charged electrons (e) and positively-charged holes (h) can exist in low-dimensional semiconductor nanostructures. In addition to the familiar exciton (e+h), three-body "charged excitons" (2e+h and 2h+e) have also been observed. Much less is known about the properties of such charged excitons since three-body problems are generally very difficult to solve, even numerically. Here we introduce a simple model, which can be considered as an extended Calogero model, to calculate analytically the energy spectra for both a charged exciton and a neutral exciton in a one-dimensional nanostructure, such as a finite-length quantum wire. Apart from its physical motivation, the model is of mathematical interest in that it can be related to the Heun (or Heine) equation and, as shown explicitly, highly accurate, closed form solutions can be obtained.

Original language | English (US) |
---|---|

Pages (from-to) | 4013-4022 |

Number of pages | 10 |

Journal | Journal of Mathematical Physics |

Volume | 38 |

Issue number | 8 |

State | Published - Aug 1997 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Mathematical Physics
- Physics and Astronomy(all)
- Statistical and Nonlinear Physics

### Cite this

*Journal of Mathematical Physics*,

*38*(8), 4013-4022.

**A solvable model for excitonic complexes in one dimension.** / Markvardsen, Anders J.; Johnson, Neil F.

Research output: Contribution to journal › Article

*Journal of Mathematical Physics*, vol. 38, no. 8, pp. 4013-4022.

}

TY - JOUR

T1 - A solvable model for excitonic complexes in one dimension

AU - Markvardsen, Anders J.

AU - Johnson, Neil F

PY - 1997/8

Y1 - 1997/8

N2 - It is known experimentally that stable few-body clusters containing negatively-charged electrons (e) and positively-charged holes (h) can exist in low-dimensional semiconductor nanostructures. In addition to the familiar exciton (e+h), three-body "charged excitons" (2e+h and 2h+e) have also been observed. Much less is known about the properties of such charged excitons since three-body problems are generally very difficult to solve, even numerically. Here we introduce a simple model, which can be considered as an extended Calogero model, to calculate analytically the energy spectra for both a charged exciton and a neutral exciton in a one-dimensional nanostructure, such as a finite-length quantum wire. Apart from its physical motivation, the model is of mathematical interest in that it can be related to the Heun (or Heine) equation and, as shown explicitly, highly accurate, closed form solutions can be obtained.

AB - It is known experimentally that stable few-body clusters containing negatively-charged electrons (e) and positively-charged holes (h) can exist in low-dimensional semiconductor nanostructures. In addition to the familiar exciton (e+h), three-body "charged excitons" (2e+h and 2h+e) have also been observed. Much less is known about the properties of such charged excitons since three-body problems are generally very difficult to solve, even numerically. Here we introduce a simple model, which can be considered as an extended Calogero model, to calculate analytically the energy spectra for both a charged exciton and a neutral exciton in a one-dimensional nanostructure, such as a finite-length quantum wire. Apart from its physical motivation, the model is of mathematical interest in that it can be related to the Heun (or Heine) equation and, as shown explicitly, highly accurate, closed form solutions can be obtained.

UR - http://www.scopus.com/inward/record.url?scp=0031481523&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0031481523&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0031481523

VL - 38

SP - 4013

EP - 4022

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

IS - 8

ER -