scholarly journals Regularity for a Schrödinger equation with singular potentials and application to bilinear optimal control

2005 ◽  
Vol 216 (1) ◽  
pp. 188-222 ◽  
Author(s):  
Lucie Baudouin ◽  
Otared Kavian ◽  
Jean-Pierre Puel
Keyword(s):  
Optimal Control ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Singular Potentials

scholarly journals Evolution by Schrödinger equation of Aharonov–Berry superoscillations in centrifugal potential

2019 ◽  
Vol 475 (2225) ◽  
pp. 20180390 ◽  
Author(s):  
F. Colombo ◽  
J. Gantner ◽  
D. C. Struppa
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Singular Potential ◽  
Singular Potentials ◽  
Limit Solution ◽  
Quadratic Hamiltonian

In recent years, we have investigated the evolution of superoscillations under Schrödinger equation with non-singular potentials. In all those cases, we have shown that superoscillations persist in time. In this paper, we investigate the centrifugal potential, which is a singular potential, and we show that the techniques developed to study the evolution of superoscillations in the case of the Schrödinger equation with a quadratic Hamiltonian apply to this setting. We also specify, in the case of the centrifugal potential, the notion of super-shift of the limit solution, a fact explained in the last section of this paper. It then becomes apparent that superoscillations are just a particular case of super-shift.

scholarly journals A Note on Optimal Control Problem Governed by Schrödinger Equation

Open Physics ◽  
2015 ◽  
Vol 13 (1) ◽  
Author(s):  
Yusuf Koçak ◽  
Ercan Çelik ◽  
Nigar Yıldırım Aksoy
Keyword(s):  
Optimal Control ◽  
Variational Inequality ◽  
Schrödinger Equation ◽  
Optimal Control Problem ◽  
Existence And Uniqueness ◽  
Schrodinger Equation ◽  
Optimal Solution ◽  
Necessary Condition ◽  
Existence And Uniqueness Theorem ◽  
The Cost

AbstractIn 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.

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