Absence of bound states in a class of time-dependent Hamiltonians
type: Item
instance of: scholarly article
title: Absence of bound states in a class of time-dependent Hamiltonians
zbMATH Open document ID: 0811.34069
author: Min-Jei Huang
published in: Journal of Mathematical Analysis and Applications
publication date: 1994-07-04T00:00:00Z
review text: This paper proves the absence of bound state solutions for the time- dependent one-dimensional Schrödinger equation. The potential \(V(x,t)\) satisfies (1) \(\partial V/ \partial x = O(x^{-\alpha})\) at infinity, with \(\alpha > 1\); (2) \(x \partial V/ \partial x \leq-(1/2) \alpha (\alpha + 1) x^{-2}\) for large \(x\), resp. \(\leq 0\) for small \(x\) (repulsivity); (3) smoothness conditions. In addition, in case \(V\) is time-periodic, it is shown that the monodromy operator has purely absolutely continuous spectrum.
reviewed by: Satyanad Kichenassamy
Mathematics Subject Classification ID: 34L40
Mathematics Subject Classification ID: 47A40
zbMATH DE Number: 599959
zbMATH Keywords: absence of bound state solutions
zbMATH Keywords: time-dependent one-dimensional Schrödinger equation
MaRDI profile type: Publication
full work available at URL: jmaa.1994.1154
OpenAlex ID: W2001631257
DOI: 10.1006/JMAA.1994.1154
description: scientific article; zbMATH DE number 599959