On the method of pseudopotential for Schrödinger equation with nonlocal boundary conditions
type: Item
instance of: scholarly article
title: On the method of pseudopotential for Schrödinger equation with nonlocal boundary conditions
zbMATH Open document ID: 1011.35043
DOI: 10.1155/S1085337501000689
author: Yu. V. Zasorin
published in: Abstract and Applied Analysis
publication date: 2003-06-12T00:00:00Z
full work available at URL: https://eudml.org/doc/49982
full work available at URL: S1085337501000689.html
review text: This paper studies the stationary Schrödinger equation \[ (\vec \nabla\cdot \vec\nabla +\lambda^2_0) \psi(\vec r)-q (\vec r,\psi, \vec\nabla \psi)=0\text{ in }\mathbb{R}^n, \tag{1} \] with finite potential \(q\). The method of pseudopotential, often used for the study of (1), is contained in replacement of the potential \(q\) by the pseudopotential \(\widehat q\), which does not depend explicitly on \(\psi\) and \(\vec\nabla\psi\). Here in contrast to methods of pseudopotential used up to now, the new method proposed does not require the knowledge of the explicit form of the potential \(q\).
Mathematics Subject Classification ID: 35J10
Mathematics Subject Classification ID: 35Q55
Mathematics Subject Classification ID: 35Q40
Mathematics Subject Classification ID: 35Q51
Mathematics Subject Classification ID: 35A25
zbMATH DE Number: 1750370
zbMATH Keywords: stationary Schrödinger equation
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
OpenAlex ID: W2090415383
description: scientific article; zbMATH DE number 1750370