# Controllability of Schrödinger equations

Karine Beauchard^{[1]}

- [1] CMLA ENS Cachan 94230 Cachan

Séminaire Équations aux dérivées partielles (2005-2006)

- Volume: 84, Issue: 7, page 1-18

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topBeauchard, Karine. "Controllability of Schrödinger equations." Séminaire Équations aux dérivées partielles 84.7 (2005-2006): 1-18. <http://eudml.org/doc/11144>.

@article{Beauchard2005-2006,

abstract = {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 time, by moving the potential well in a suitable way.The proof uses moment theory, a Nash-Moser theorem, Coron’s return method and expansions to the second order.This article summarizes two works : [4] and a joint work with Jean-Michel Coron [5].},

affiliation = {CMLA ENS Cachan 94230 Cachan},

author = {Beauchard, Karine},

journal = {Séminaire Équations aux dérivées partielles},

language = {eng},

number = {7},

pages = {1-18},

publisher = {Centre de mathématiques Laurent Schwartz, École polytechnique},

title = {Controllability of Schrödinger equations},

url = {http://eudml.org/doc/11144},

volume = {84},

year = {2005-2006},

}

TY - JOUR

AU - Beauchard, Karine

TI - Controllability of Schrödinger equations

JO - Séminaire Équations aux dérivées partielles

PY - 2005-2006

PB - Centre de mathématiques Laurent Schwartz, École polytechnique

VL - 84

IS - 7

SP - 1

EP - 18

AB - 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 time, by moving the potential well in a suitable way.The proof uses moment theory, a Nash-Moser theorem, Coron’s return method and expansions to the second order.This article summarizes two works : [4] and a joint work with Jean-Michel Coron [5].

LA - eng

UR - http://eudml.org/doc/11144

ER -

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