A novel numerical technique for solving the one-dimensional Schroedinger equation using matrix approach-application to quantum well structures

Author

Ghatak, Ajoy K. ; Thyagarajan, K. ; Shenoy, M.R.

Author_Institution

Dept. of Phys., Indian Inst. of Technol., New Delhi, India

Volume

24

Issue

8

fYear

1988

fDate

8/1/1988 12:00:00 AM

Firstpage

1524

Lastpage

1531

Abstract

A numerical technique that allows straightforward determination of bound-state and quasi-bound-state energy eigenvalues (and lifetimes of the latter) for arbitrary one-dimensional potentials is presented. The method involves straightforward multiplication of 2×2 matrices and does not involve any iterations. The applicability of the technique to analysis of the quantum-well structures is also shown. Since the Schroedinger equation for a spherically symmetric potential can be transformed to a one-dimensional equation, all such problems can also be solved using this method

Keywords

Schrodinger equation; eigenvalues and eigenfunctions; matrix algebra; numerical methods; semiconductor junctions; 2×2 matrices; bound-state energy eigenvalues; numerical technique; quasi-bound-state energy eigenvalues; Eigenvalues and eigenfunctions; Equations; Optical device fabrication; Optical devices; Optical materials; Optical superlattices; Potential well; Symmetric matrices; Transmission line matrix methods; Wave functions;

fLanguage

English

Journal_Title

Quantum Electronics, IEEE Journal of

Publisher

ieee

ISSN

0018-9197

Type

jour

DOI

10.1109/3.7079

Filename

7079