Quasi-conical quantum dot: electron states and quantum transitions

TL;DR

This paper introduces an exactly solvable model of a quasi-conical quantum dot with spherical sector geometry, providing analytical solutions for electron states and quantum transitions, and compares results with existing models.

Contribution

It presents a new solvable model of a quasi-conical quantum dot with analytical wave functions and energy spectra, extending understanding of quantum states in such geometries.

Findings

Analytical expressions for wave functions and energy spectra are derived.

The model reduces to the conical quantum dot case at small sector angles.

Quantum transitions are analyzed within this new model.

Abstract

The exactly solvable model of quasi-conical quantum dot, having a form of spherical sector is proposed. Due to the specific symmetry of the problem the separation of variables in spherical coordinates is possible in the one-electron Schrodinger equation. Analytical expressions for wave function and energy spectrum are obtained. It is shown that at small values of the stretch angle of spherical sector the problem reduced to the conical QD problem. The comparison with previously performed works showed good agreement of results. As an application of the obtained results, the quantum transitions in the system are considered.