Accurate solutions to Schrodinger´s equation using modified Airy functions

Author

Ghatak, A.K. ; Gallawa, R.L. ; Goyal, I.C.

Author_Institution

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

Volume

28

Issue

2

fYear

1992

fDate

2/1/1992 12:00:00 AM

Firstpage

400

Lastpage

403

Abstract

A formulation that utilizes the Airy functions is applied to Schrodinger´s equation for a spherically symmetric potential. It is shown that the computational procedure is very simple and allows a very accurate description of bound-state wave functions and the corresponding eigenvalues. It is also demonstrated that the eigenvalues can be determined from the tabulated zeros of the Airy function with as much ease as the WKB method affords. In composing this modified Airy function solution to the WKB solution for the wave function, the first-order solution in each case is used

Keywords

Schrodinger equation; eigenvalues and eigenfunctions; optical waveguide theory; quantum optics; wave functions; Schrodinger equation; WKB method; WKB solution; bound-state wave functions; computational procedure; eigenvalues; first-order solution; modified Airy functions; optical waveguide theory; quantum mechanics; spherically symmetric potential; tabulated zeros; wave function; Eigenvalues and eigenfunctions; Microcomputers; Optical waveguide theory; Optical waveguides; Optimization methods; Physics; Schrodinger equation; Turning; US Department of Commerce; Wave functions;

fLanguage

English

Journal_Title

Quantum Electronics, IEEE Journal of

Publisher

ieee

ISSN

0018-9197

Type

jour

DOI

10.1109/3.123265

Filename

123265