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Limitations on the control of Schrödinger equations

Reinhard IllnerHorst LangeHolger Teismann — 2006

ESAIM: Control, Optimisation and Calculus of Variations

We give the definitions of exact and approximate controllability for linear and nonlinear Schrödinger equations, review fundamental criteria for controllability and revisit a classical “No-go” result for evolution equations due to Ball, Marsden and Slemrod. In Section 2 we prove corresponding results on non-controllability for the linear Schrödinger equation and distributed additive control, and we show that the Hartree equation of quantum chemistry with bilinear control ( E ( t ) · x ) u is not controllable...

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