Spectral properties of Schrödinger operators and time-decay of the wave functions. Results in \(L^ 2(R^ 4)\)
type: Item
instance of: scholarly article
title: Spectral properties of Schrödinger operators and time-decay of the wave functions. Results in \(L^ 2(R^ 4)\)
zbMATH Open document ID: 0564.35024
DOI: 10.1016/0022-247X(84)90110-0
author: Arne Jensen
published in: Journal of Mathematical Analysis and Applications
publication date: 1984-01-01T00:00:00Z
review text: The author considers Schrödinger operators \(H=-\Delta +V\) in \(L^ 2({\mathbb{R}}^ 4)\), where \(V(x)=O(| x|^{-\beta})\) as \(| x| \to \infty\) for some \(\beta >0\). Furthermore some local singularities are permitted. He is concerned with the spectral properties of H in the low energy limit. The results are expressed in terms of asymptotic expansions for the resolvent \(R(\zeta)=(H-\zeta)^{-1}\) as \(\zeta\) \(\to 0\).
Mathematics Subject Classification ID: 35J10
Mathematics Subject Classification ID: 35Q99
Mathematics Subject Classification ID: 35P05
Mathematics Subject Classification ID: 81Q10
zbMATH DE Number: 3899384
zbMATH Keywords: Schrödinger operators
zbMATH Keywords: local singularities
zbMATH Keywords: spectral properties
zbMATH Keywords: low energy limit
zbMATH Keywords: asymptotic expansions
zbMATH Keywords: resolvent
MaRDI profile type: Publication
cites work: Q5558293
cites work: Q3232397
cites work: Q5724171
cites work: Q5799009
cites work: Spectral properties of Schrödinger operators and time-decay of the wave functions
cites work: Spectral properties of Schrödinger operators and time-decay of the wave functions results in \(L^2(\mathbb{R}^m),\;m\geq 5\)
cites work: Coupling constant thresholds in nonrelativistic quantum mechanics. I. Short-range two-body case
cites work: Q4185363
cites work: ON EXTERIOR ELLIPTIC PROBLEMS POLYNOMIALLY DEPENDING ON A SPECTRAL PARAMETER, AND THE ASYMPTOTIC BEHAVIOR FOR LARGE TIME OF SOLUTIONS OF NONSTATIONARY PROBLEMS
cites work: ON THE SHORT WAVE ASYMPTOTIC BEHAVIOUR OF SOLUTIONS OF STATIONARY PROBLEMS AND THE ASYMPTOTIC BEHAVIOUR ASt→ ∞ OF SOLUTIONS OF NON-STATIONARY PROBLEMS
cites work: Asymptotic expansions in time for solutions of Schrödinger-type equations
description: scientific article; zbMATH DE number 3899384