# Simple correlated wave-functions for excitons in 0D, quasi-1D and quasi-2D quantum dots

## TL;DR

This paper introduces simple, parameter-dependent correlated wave-functions for excitons in various quantum dot geometries, providing analytical formulas and efficient integration methods for Coulomb interactions.

## Contribution

It presents a novel, straightforward wave-function model with analytical normalization and energy formulas, applicable to 0D, quasi-1D, and quasi-2D quantum dots.

## Key findings

- Analytical formulas for wave-function normalization and energies.
- Fast integration methods for Coulomb interactions in different geometries.
- Applicable to excitons in various quantum dot dimensions.

## Abstract

We propose correlated yet extremely simple single-parameter-dependent wave-functions with a Slater-type correlation factor, to describe excitons in 0D, quasi-1D and quasi-2D semiconductor quantum dots. We provide closed-form formulas for the wave-function normalization factor, electron/hole single-particle density and the expectation value of the kinetic energy. We additionally supply fast integration procedures for the Coulomb interaction in the presence of dielectric mismatch with the surrounding medium for nanoplatelets (quasi-2D systems), and for the bare-Coulomb integral in long nanorods (quasi-1D systems).