The variational formulation of an inverse problem for multidimensional nonlinear time-dependent Schrödinger equation

AbstractIn this paper, an inverse problem of determining the unknown coefficient of a multidimensional nonlinear time-dependent Schrödinger equation that has a complex number at nonlinear part is considered. The inverse problem is reformulated as a variational one which aims to minimize the observation functional. This paper presents existence and uniqueness theorems of solutions of the constituted variational problem, the gradient of the observation functional and a necessary condition for the solution of the variational problem.

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Stability estimate for an inverse problem for the Schrödinger equation in a magnetic field with time-dependent coefficient

Journal of Mathematical Physics ◽

10.1063/1.4995606 ◽

2017 ◽

Vol 58 (7) ◽

pp. 071508 ◽

Cited By ~ 5

Author(s):

Ibtissem Ben Aïcha

Keyword(s):

Magnetic Field ◽

Inverse Problem ◽

Schrödinger Equation ◽

Schrodinger Equation ◽

Stability Estimate ◽

Time Dependent

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A Note on Optimal Control Problem Governed by Schrödinger Equation

Open Physics ◽

10.1515/phys-2015-0051 ◽

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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On the Schrödinger equation with time-dependent electric fields

Proceedings of the Royal Society of Edinburgh Section A Mathematics ◽

10.1017/s0308210500020527 ◽

1984 ◽

Vol 96 (1-2) ◽

pp. 117-134 ◽

Cited By ~ 10

Author(s):

Rafael José Iório ◽

Dan Marchesin

Keyword(s):

Schrödinger Equation ◽

Electric Fields ◽

Existence And Uniqueness ◽

Schrodinger Equation ◽

Short Range ◽

Bound States ◽

Time Dependent ◽

Uniqueness Of Solutions ◽

Wave Operators

SynopsisWe prove existence and uniqueness of solutions of i(∂ψ/∂t) = (−Δ+x1g(t)+q(x))ψ, ψ(x, s) = ψs (x) in ℝ3 for potentials q(x) including the Coulomb case. Existence and completeness of the wave operators is established for g(t) periodic with zero mean and q(x) short-range, smooth in the x1 direction. We characterize scattering and bound states in terms of the period operator.

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Introduction

10.1093/oso/9780198805014.003.0001 ◽

2018 ◽

Author(s):

Niels Engholm Henriksen ◽

Flemming Yssing Hansen

Keyword(s):

Schrödinger Equation ◽

Schrodinger Equation ◽

Degrees Of Freedom ◽

State Level ◽

Boltzmann Distribution ◽

Theoretical Description ◽

Time Dependent ◽

Nuclear Dynamics ◽

Molecular Reaction ◽

Oppenheimer Approximation

This introductory chapter considers first the relation between molecular reaction dynamics and the major branches of physical chemistry. The concept of elementary chemical reactions at the quantized state-to-state level is discussed. The theoretical description of these reactions based on the time-dependent Schrödinger equation and the Born–Oppenheimer approximation is introduced and the resulting time-dependent Schrödinger equation describing the nuclear dynamics is discussed. The chapter concludes with a brief discussion of matter at thermal equilibrium, focusing at the Boltzmann distribution. Thus, the Boltzmann distribution for vibrational, rotational, and translational degrees of freedom is discussed and illustrated.

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