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

2017 ◽  
Vol 58 (7) ◽  
pp. 071508 ◽  
Author(s):  
Ibtissem Ben Aïcha
Keyword(s):  
Magnetic Field ◽  
Inverse Problem ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Stability Estimate ◽  
Time Dependent

scholarly journals A Hölder-logarithmic stability estimate for an inverse problem in two dimensions

2015 ◽  
Vol 23 (1) ◽  
Author(s):  
Matteo Santacesaria
Keyword(s):  
Inverse Problem ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Stability Estimate ◽  
Two Dimensions ◽  
Positive Energy ◽  
Two Dimensional ◽  
Ill Posed ◽  
Dirichlet To Neumann Map ◽  
Logarithmic Stability

AbstractThe problem of the recovery of a real-valued potential in the two-dimensional Schrödinger equation at positive energy from the Dirichlet-to-Neumann map is considered. It is know that this problem is severely ill-posed and the reconstruction of the potential is only logarithmic stable in general. In this paper a new stability estimate is proved, which is explicitly dependent on the regularity of the potentials and on the energy. Its main feature is an efficient

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

2016 ◽  
Vol 24 (5) ◽  
Author(s):  
Nigar Yıldırım Aksoy
Keyword(s):  
Inverse Problem ◽  
Schrödinger Equation ◽  
Variational Problem ◽  
Existence And Uniqueness ◽  
Variational Formulation ◽  
Schrodinger Equation ◽  
Time Dependent ◽  
Unknown Coefficient ◽  
Necessary Condition ◽  
Nonlinear Part

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.

scholarly journals Simultaneous determination of the magnetic field and the electric potential in the Schrödinger equation by a finite number of boundary observations

2018 ◽  
Vol 26 (2) ◽  
pp. 201-209 ◽  
Author(s):  
Ibtissem Ben Aïcha ◽  
Youssef Mejri
Keyword(s):  
Magnetic Field ◽  
Schrödinger Equation ◽  
Finite Number ◽  
Electric Potential ◽  
Schrodinger Equation ◽  
Initial Conditions ◽  
Stability Estimate ◽  
Lipschitz Stability ◽  
The Magnetic Field

AbstractWe study the inverse problem of determining the magnetic field and the electric potential appearing in the magnetic Schrödinger equation from the knowledge of a finite number of lateral observations of the solution. We prove a Lipschitz stability estimate for both coefficients simultaneously by choosing the “initial” conditions suitably.

Introduction

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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