Open AccessEXACT SOLUTION OF SCHR?DINGER EQUATION WITH REFLECTIONLESS POTENTIAL WELL
Author(s) -
Guanghui Zhou
Publication year - 1993
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.42.173
Subject(s) - eigenfunction , legendre polynomials , normalization (sociology) , legendre function , associated legendre polynomials , scattering , transformation (genetics) , physics , legendre transformation , schrödinger equation , legendre's equation , woods–saxon potential , exact solutions in general relativity , mathematical analysis , mathematical physics , eigenvalues and eigenvectors , mathematics , quantum mechanics , orthogonal polynomials , classical orthogonal polynomials , biochemistry , gegenbauer polynomials , chemistry , sociology , anthropology , gene
Using a transformation of hyperbolic function, the Schr?dinger equation with reflection-less potential well is transformed into an associated-Legendre equation. Then both bound and scattering state eigenfunctions are expressed in terms of associated-Legendre polynomials and functions respectively. The exact solutions obtained in this paper are more general and systematic than some asymptotic solutions or solutions of reflectionless potential with special parameters in literatures. The normalization of the scattering state is discussed in detail.