On the ambiguous treatment of the Schrödinger equation for the infinite potential well and an alternative via flat solutions: the one-dimensional case
type: Item
instance of: scholarly article
title: On the ambiguous treatment of the Schrödinger equation for the infinite potential well and an alternative via flat solutions: the one-dimensional case
zbMATH Open document ID: 1328.81101
DOI: 10.4171/IFB/345
published in: Interfaces and Free Boundaries
publication date: 2015-12-30T00:00:00Z
review text: Summary: An ambiguity in the mathematical treatment of the study of bound state solutions of the Schrödinger equation for infinite well type potentials (studied for the first time in a pioneering article of 1928 by \textit{G. Gamow} [Z. Phys. 51, 204--212 (1928; JFM 54.0969.04)]) is pointed out. An alternative to prove a similar ``localizing effect'' is here offered ``in terms Hardy type potentials'' with the distance to the boundary as a variable. The existence of flat solutions (with zero normal derivative at the boundary) and solutions with compact support is here obtained by first time in the literature for elliptic problems for this kind of linear equations.
Mathematics Subject Classification ID: 81Q05
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 35R35
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 35Q40
zbMATH DE Number: 6524744
zbMATH Keywords: Schrödinger equation
zbMATH Keywords: infinite well potential
zbMATH Keywords: Hardy potentials
zbMATH Keywords: sublinear eigenvalue type problem
zbMATH Keywords: flat solution
zbMATH Keywords: solution with compact support
author: J. I. Díaz
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 6524744