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.

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.

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.

Numerical Solution of the Time-Dependent Schrödinger Equation and Application toH+-H

1979 ◽  
Vol 43 (7) ◽  
pp. 512-515 ◽  
Author(s):  
Vida Maruhn-Rezwani ◽  
Norbert Grün ◽  
Werner Scheid
Keyword(s):  
Schrödinger Equation ◽  
Numerical Solution ◽  
Schrodinger Equation ◽  
Time Dependent
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