scholarly journals On form-preserving transformations for the time-dependent Schrödinger equation

1999 ◽  
Vol 40 (7) ◽  
pp. 3268-3274 ◽  
Author(s):  
Federico Finkel ◽  
Artemio González-López ◽  
Niky Kamran ◽  
Miguel A. Rodrı́guez
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Time Dependent

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

Schrödinger dynamics and optimal transport of measures

2021 ◽  
pp. 2150016
Author(s):  
Lorenzo Zanelli
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Transport Theory ◽  
Optimal Transport ◽  
Time Dependent ◽  
Probability Measures ◽  
Flat Torus ◽  
Optimal Transport Theory

In this paper, we recover a class of displacement interpolations of probability measures, in the sense of the Optimal Transport theory, by means of semiclassical measures associated with solutions of Schrödinger equation defined on the flat torus. Moreover, we prove the completing viewpoint by proving that a family of displacement interpolations can always be viewed as a path of time-dependent semiclassical measures.

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