Quasi-exact solvability of a hyperbolic intermolecular potential induced by an effective mass step
type: Item
instance of: scholarly article
title: Quasi-exact solvability of a hyperbolic intermolecular potential induced by an effective mass step
zbMATH Open document ID: 1227.34090
DOI: 10.1155/2011/358198
author: Axel Schulze-Halberg
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2011-05-27T00:00:00Z
full work available at URL: https://eudml.org/doc/230588
review text: Consider the stationary Schrödinger equation \[ {1\over 2m(x)}\psi''(x)- {m'(x)\over 2m^2(x)} \psi'(x)+ (E- V(x))\psi(x)= 0\tag{\(*\)} \] with \[ \begin{gathered} m(x)= 1+ 1+\tanh(x),\\ V(x; a,b,c,d)= a\tanh(x)+ b\tanh^2(x)+ c\tanh^3(x)+ d,\\ E= b-a+ d-c.\end{gathered} \] The author establishes explicit solutions of \((*)\) and derives conditions for their \(L^2\)-normalizability.
reviewed by: Klaus R. Schneider
Mathematics Subject Classification ID: 34L40
Mathematics Subject Classification ID: 34A05
zbMATH DE Number: 5900717
Wikidata QID: Q58687765
MaRDI profile type: Publication
OpenAlex ID: W1997249882
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DBLP publication ID: journals/ijmmsc/Schulze-Halberg11
description: scientific article; zbMATH DE number 5900717