Absence of point spectrum for unitary operators

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:244

Article

Astaburuaga, M. A.¹  Bourget, O.¹  Cortes, V. H.¹  Fernandez, C.¹ 

[1] Pontificia Univ Catolica Chile, Fac Matemat, Santiago, Chile

关键词: point spectrum;    propagator;    commutator;    Schrodinger equation;   

DOI  :  10.1016/j.jde.2007.10.025

来源: Elsevier

【 摘 要 】

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.

【 授权许可】

Free