Limitations on the 
control of 
Schrödinger equations

Reinhard Illner; Horst Lange; Holger Teismann

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One considers a quantum particle in a 1D moving infinite square potential well. It is a nonlinear control system in which the state is the wave function of the particle and the control is the acceleration of the potential well. One proves the local controllability around any eigenstate, and the steady state controllability (controllability between eigenstates) of this control system. In particular, the wave function can be moved from one eigenstate to another one, exactly and in finite...

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In this Note, applying our recent Theorem 3.1 of [7], we prove that suitable perturbations of a completely controllable linear control system, do not affect the controllability of the system.

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Karine Beauchard (2008)

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We consider a quantum particle in a 1D infinite square potential well with variable length. It is a nonlinear control system in which the state is the wave function $φ$ of the particle and the control is the length $l (t)$ of the potential well. We prove the following controllability result : given $φ_{0}$ close enough to an eigenstate corresponding to the length $l = 1$ and $φ_{f}$ close enough to another eigenstate corresponding to the length $l = 1$ , there exists a continuous function $l : [0, T] \to ℝ_{+}^{*}$ with $T > 0$ , such that $l (0) = 1$ and $l (T) = 1$ ,...