SPECTRAL PROPERTIES OF A COUPLED SYSTEM OF SCHRODINGER EQUATIONS WITH TIME-PERIODIC COEFFICIENTS
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Date
2012
Journal Title
Journal ISSN
Volume Title
Publisher
KHAYYAM PUBL CO INC
Abstract
We consider a coupled system of Schrodinger equations with time-periodic coefficients
i u(t) = -Delta u + V(x, t)u + g(x, t)v
i v(t) = -Delta v + W(x, t)v + g(x, t)u
on the Hilbert space H = L(2)(R(n)) x L(2)(R(n)), where g, V and W are periodic time-dependent potentials, with period T. We denote by (U(t, s))((t, s)is an element of RxR) its associated propagator. By using a multiplier method, we rule out the existence of regular eigenvectors of the Floquet operator U(T, 0).
i u(t) = -Delta u + V(x, t)u + g(x, t)v
i v(t) = -Delta v + W(x, t)v + g(x, t)u
on the Hilbert space H = L(2)(R(n)) x L(2)(R(n)), where g, V and W are periodic time-dependent potentials, with period T. We denote by (U(t, s))((t, s)is an element of RxR) its associated propagator. By using a multiplier method, we rule out the existence of regular eigenvectors of the Floquet operator U(T, 0).
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Keywords
SCATTERING-THEORY, DEPENDENT HAMILTONIANS