A Note on Optimal Control Problem Governed by Schrödinger Equation

• Autorzy: Yusuf Koçak , Ercan Çelik , Nigar Yıldırım Aksoy
• Języki publikacji: EN

Abstrakty

EN

In this work, we present some results showing the controllability of the linear Schrödinger equation with complex potentials. Firstly we investigate the existence and uniqueness theorem for solution of the considered problem. Then we find the gradient of the cost functional with the help of Hamilton-Pontryagin functions. Finally we state a necessary condition in the form of variational inequality for the optimal solution using this gradient.

Słowa kluczowe

EN

Schrödinger equation; Optimal Control; Hamilton-Pontryagin functions; Fréchet derivative

• Czasopismo: Open Physics
• Rocznik: 2015
• Tom: 13
• Numer: 1

Daty

otrzymano

2015-09-28

zaakceptowano

2015-11-26

online

2015-12-31

Twórcy

autor

Yusuf Koçak

• Department of Mathematics,
  Ağrı İbrahim Çeçen Universty,Faculty of Science and
  Art,Ağrı,Turkey

autor

Ercan Çelik

• Department of Mathematics, Ataturk University,
  Faculty of Science, Erzurum, Turkey

autor

Nigar Yıldırım Aksoy

• Department of Mathematics, Kafkas University,
  Faculty of Science and Art, Kars, Turkey

Bibliografia

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Identyfikatory

DOI

10.1515/phys-2015-0051