Absence of point spectrum for unitary operators
Loading...
Date
2008
Journal Title
Journal ISSN
Volume Title
Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
Abstract
Let us consider the time-dependent Schrodinger equation,
i phi(t) = -Delta phi + V (x, t)phi,
on the Hilbert space L-2(R-n), where V (x, t) is a repulsive periodic time-dependent potential, with period T. We denote by (U(t, s))((t,s)is an element of RxR) its associated propagator. First, using a multiplier method, we rule out the existence of regular eigenvectors of the Floquet operator U(T, 0). Secondly, strengthening the hypotheses on the potential V, we prove that the spectrum of U(T, 0) does not contain any eigenvalues, by means of positive commutator methods. (c) 2007 Elsevier Inc. All rights reserved.
i phi(t) = -Delta phi + V (x, t)phi,
on the Hilbert space L-2(R-n), where V (x, t) is a repulsive periodic time-dependent potential, with period T. We denote by (U(t, s))((t,s)is an element of RxR) its associated propagator. First, using a multiplier method, we rule out the existence of regular eigenvectors of the Floquet operator U(T, 0). Secondly, strengthening the hypotheses on the potential V, we prove that the spectrum of U(T, 0) does not contain any eigenvalues, by means of positive commutator methods. (c) 2007 Elsevier Inc. All rights reserved.
Description
Keywords
point spectrum, propagator, commutator, Schrodinger equation, TIME-DEPENDENT HAMILTONIANS, SCATTERING THEORY