Analytical Solutions of the Schrödinger Equation with Power Potentials

Jacek Karwowski; Henryk A. Witek

doi:10.1002/jccs.201400540

Analytical Solutions of the Schrödinger Equation with Power Potentials

Jacek Karwowski^*, Henryk A. Witek

^*Corresponding author for this work

Department of Applied Chemistry

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

Conditions for the existence of polynomial solutions of the Schrödinger equation with potentials which are linear combinations of powers of r ranging from -2 to 2m, where m is a non-negative integer, are derived and explicit expressions for the coefficients are given. Potentials with m = 0, 1, 2 are discussed in detail.

Original language	English
Pages (from-to)	101-108
Number of pages	8
Journal	Journal of the Chinese Chemical Society
Volume	63
Issue number	1
DOIs	https://doi.org/10.1002/jccs.201400540
State	Published - Jan 2016

Keywords

Exact solubility
Hessenberg determinant
Heun equation
Power potentials
Quasi-exact solubility
Schrödinger equation

Access to Document

10.1002/jccs.201400540

Cite this

@article{fc307450062a42f99be9af18a0d713c3,

title = "Analytical Solutions of the Schr{\"o}dinger Equation with Power Potentials",

abstract = "Conditions for the existence of polynomial solutions of the Schr{\"o}dinger equation with potentials which are linear combinations of powers of r ranging from -2 to 2m, where m is a non-negative integer, are derived and explicit expressions for the coefficients are given. Potentials with m = 0, 1, 2 are discussed in detail.",

keywords = "Exact solubility, Hessenberg determinant, Heun equation, Power potentials, Quasi-exact solubility, Schr{\"o}dinger equation",

author = "Jacek Karwowski and Witek, {Henryk A.}",

year = "2016",

month = jan,

doi = "10.1002/jccs.201400540",

language = "English",

volume = "63",

pages = "101--108",

journal = "Journal of the Chinese Chemical Society",

issn = "0009-4536",

publisher = "Wiley-Blackwell",

number = "1",

}

TY - JOUR

T1 - Analytical Solutions of the Schrödinger Equation with Power Potentials

AU - Karwowski, Jacek

AU - Witek, Henryk A.

PY - 2016/1

Y1 - 2016/1

N2 - Conditions for the existence of polynomial solutions of the Schrödinger equation with potentials which are linear combinations of powers of r ranging from -2 to 2m, where m is a non-negative integer, are derived and explicit expressions for the coefficients are given. Potentials with m = 0, 1, 2 are discussed in detail.

AB - Conditions for the existence of polynomial solutions of the Schrödinger equation with potentials which are linear combinations of powers of r ranging from -2 to 2m, where m is a non-negative integer, are derived and explicit expressions for the coefficients are given. Potentials with m = 0, 1, 2 are discussed in detail.

KW - Exact solubility

KW - Hessenberg determinant

KW - Heun equation

KW - Power potentials

KW - Quasi-exact solubility

KW - Schrödinger equation

UR - http://www.scopus.com/inward/record.url?scp=84956843944&partnerID=8YFLogxK

U2 - 10.1002/jccs.201400540

DO - 10.1002/jccs.201400540

M3 - Article

AN - SCOPUS:84956843944

SN - 0009-4536

VL - 63

SP - 101

EP - 108

JO - Journal of the Chinese Chemical Society

JF - Journal of the Chinese Chemical Society

IS - 1

ER -

Analytical Solutions of the Schrödinger Equation with Power Potentials

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this