Solution existence and uniqueness for degenerate SDEs with application to Schrödinger-equation representations

2021 ◽  
Vol 21 (2) ◽  
pp. 297-315
Author(s):  
Peter M. Dower ◽  
Hidehiro Kaise ◽  
William M. McEneaney ◽  
Tao Wang ◽  
Ruobing Zhao
Keyword(s):  
Schrödinger Equation ◽  
Existence And Uniqueness ◽  
Schrodinger Equation ◽  
Solution Existence ◽  
Solution Existence And Uniqueness

Solution existence and uniqueness for degenerate SDEs with application to Schrödinger-equation representations

2021 ◽  
Vol 21 (2) ◽  
pp. 297-315
Author(s):  
Peter M. Dower ◽  
Hidehiro Kaise ◽  
William M. McEneaney ◽  
Tao Wang ◽  
Ruobing Zhao
Keyword(s):  
Schrödinger Equation ◽  
Existence And Uniqueness ◽  
Schrodinger Equation ◽  
Solution Existence ◽  
Solution Existence And Uniqueness

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.

scholarly journals The Solvability of First Type Boundary Value Problem for a Schrödinger Equation

2020 ◽  
Vol 5 (1) ◽  
pp. 211-220
Author(s):  
Nigar Yildirim Aksoy
Keyword(s):  
Schrödinger Equation ◽  
Boundary Value Problem ◽  
Existence And Uniqueness ◽  
Schrodinger Equation ◽  
Boundary Value ◽  
A Priori ◽  
A Priori Estimate ◽  
Uniqueness Theorems ◽  
Priori Estimate ◽  
Type Boundary

AbstractThe paper presents an first type boundary value problem for a Schrödinger equation. The aim of paper is to give the existence and uniqueness theorems of the boundary value problem using Galerkin’s method. Also, a priori estimate for its solution is given.

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.

On the Schrödinger equation with time-dependent electric fields

1984 ◽  
Vol 96 (1-2) ◽  
pp. 117-134 ◽  
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.

Sign in / Sign up

Export Citation Format

Share Document