Explicit higher-dimensional Darboux transformations for the time-dependent Schrödinger equation

2012 ◽  
pp. 165-180
Author(s):  
Axel Schulze-Halberg
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Time Dependent ◽  
Darboux Transformations ◽  
Higher Dimensional

EFFECTIVE MASS HAMILTONIANS WITH LINEAR TERMS IN THE MOMENTUM: DARBOUX TRANSFORMATIONS AND FORM-PRESERVING TRANSFORMATIONS

2007 ◽  
Vol 22 (08n09) ◽  
pp. 1735-1769 ◽  
Author(s):  
AXEL SCHULZE-HALBERG
Keyword(s):  
Wave Function ◽  
Schrödinger Equation ◽  
Effective Mass ◽  
Schrodinger Equation ◽  
Time Dependent ◽  
Darboux Transformations

We define form-preserving transformations and Darboux transformations for time-dependent, effective mass Hamiltonians with additional linear terms. We give reality conditions for both transformations, guaranteeing the transformed potential to be real-valued. We further show that our form-preserving transformation preserves normalizability of the Schrödinger wave function. Our results generalize all former results on form-preserving transformations and Darboux transformations for the time-dependent Schrödinger equation. This paper is a sequel of Refs. 16–18.

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

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
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