The envelope theory as a pedagogical tool
| Autor: | Semay, Claude, Balcaen, Maud |
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| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | Eur. J. Phys. 44 (2023) 035401 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1088/1361-6404/acbe7d |
| Popis: | The envelope theory is a reliable and easy to implement method to solve time independent Schr\"odinger-like equations (eigenvalues and eigenvectors). It is particularly useful to solve many-body systems since the computational cost is independent from the number of particles. The purpose of this paper is twofold. First, we want to make known a method that is probably too little used. Second, we also want to show that this method can be used as a pedagogical tool, thanks to its simplicity and the reliable results that can be obtained. To reach these goals, the envelope theory is applied to a simple problem in one dimension, the soft-Coulomb potential $-k/\sqrt{x^2+d^2}$, characterised by a bias distance $d$. Such interaction is used for the study of excitons, electron-hole bound pairs where the two charges are kept separated in two different one-dimensional regions (quantum wires). In addition to its physical interest, this system has never been treated with the envelope theory. Comment: https://notebookarchive.org/the-envelope-theory-as-a-pedagogical-tool--2023-03-97cajed/ |
| Databáze: | arXiv |
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