Control of the bilinear Schrödinger equation for fully coupling potentials
نویسندگان
چکیده
We present a general result of approximate controllability for the bilinear Schrödinger equation (with wave function varying in the unit sphere of an infinite dimensional Hilbert space), under the hypothesis that the Schrödinger operator has discrete spectrum and that the control potential couples all eigenstates. The control method is based on a tracking procedure for the Galerkin approximations, lifted in SU(n). The method allows to estimate the L norm of the control laws achieving controllability.
منابع مشابه
Controllability of the bilinear Schrödinger equation with several controls and application to a 3D molecule
We show the approximate rotational controllability of a polar linear molecule by means of three nonresonant linear polarized laser fields. The result is based on a general approximate controllability result for the bilinear Schrödinger equation, with wavefunction varying in the unit sphere of an infinite-dimensional Hilbert space and with several control potentials, under the assumption that th...
متن کاملGeneric controllability of the bilinear Schrödinger equation on 1-D domains: the case of measurable potentials
Several sufficient conditions for the controllability of the Schrödinger equation have been proposed in the last few years. In this article we discuss the genericity of these conditions with respect to the variation of the controlled or the uncontrolled potential. In the case where the Schrödinger equation is set on a domain of dimension one, we improve the results in the literature, removing f...
متن کاملControllability in projection of the simple spectrum bilinear Schrödinger equation
We consider the bilinear Schrödinger equation with several controls and simplespectrum drift. Under some regularity assumptions on the control operators and generic conditions on the controllability of the Galerkin approximations we show exact controllability in projection on the first n given eigenstates, n ∈ N arbitrary. Our methods rely on Lie-algebraic control techniques applied to the Gale...
متن کاملExact controllability in projections of the bilinear Schrödinger equation∗
We consider the bilinear Schrödinger equation with discrete-spectrum drift. We show, for n ∈ N arbitrary, exact controllability in projections on the first n given eigenstates. The controllability result relies on a generic controllability hypothesis on some associated finite-dimensional approximations. The method is based on Lie-algebraic control techniques applied to the finite-dimensional ap...
متن کاملRemarks on the controllability of the Schrödinger equation
In this paper we present some results on the controllability of the Schrödinger equation. We first discuss the controllability of the linear equation with a control distributed along a subdomain or subset of the boundary of the domain where the equation holds. We also analyze some possible extensions to semilinear equations in which the nonlinearity involves the state equation but the control e...
متن کامل