A GAUSSIAN WAVEPACKET APPROACH FOR CURVE-CROSSING DYNAMICS

2006 ◽  
Vol 05 (02) ◽  
pp. 207-222
Author(s):  
CHRISTOPHER A. TATE ◽  
MICHAEL MESSINA
Keyword(s):  
Probability Density ◽  
Present Method ◽  
Schrodinger Equation ◽  
Numerical Results ◽  
Time Dependent ◽  
Exact Results ◽  
Hartree Approximation ◽  
Trial Solution ◽  
Break Up ◽  
Curve Crossing

We present a Gaussian wavepacket approach for curve-crossing dynamics that only requires a single Gaussian wavepacket per surface. Unlike other Gaussian wavepacket approaches to curve-crossing dynamics, the present method does not rely upon probability density being built up on a non-adiabatically coupled surface by the break-up of an evolving wavepacket. Thus, our trial solution for the time-dependent Schrodinger equation comprised of a single Gaussian wavepacket per non-adiabatically coupled surface. We also present a generalization of the method to treat multi-dimensional systems that is based on the time-dependent Hartree approximation. We present numerical results for both single and multi-dimensional curve-crossing dynamics and compare them to the exact results.

Comparison of WKB (Wentzel–Kramers–Brillouin) and SWKB solutions of Fokker–Planck equations with exact results; application to electron thermalization

1991 ◽  
Vol 69 (6) ◽  
pp. 712-719 ◽  
Author(s):  
Bernie Shizgal ◽  
Lucio Demeio
Keyword(s):  
Schrödinger Equation ◽  
Probability Distribution Function ◽  
Schrodinger Equation ◽  
Inert Gases ◽  
Time Dependent ◽  
Exact Results ◽  
The One ◽  
Semiclassical Approximations ◽  
Fokker Planck Equations ◽  
Fokker Planck

A comparison of WKB (Wentzel–Kramers–Brillouin) and SWKB eigenfunctions of the Schrödinger equation for potentials in the class encountered in supersymmetric quantum mechanics is presented. The potentials that are studied are those that result from the transformation of a Fokker–Planck eigenvalue problem to a Schrödinger equation. Linear Fokker–Planck equations of the type considered in this paper give the probability distribution function for a large number of physical situations. The time-dependent solutions can be expressed as a sum of exponential terms with each term characterized by an eigenvalue of the Fokker–Planck operator. The specific Fokker–Planck operator considered is the one that describes the thermalization of electrons in the inert gases. The WKB and SWKB semiclassical approximations are compared with exact numerical results. Although the eigenvalues can be very close to the exact values, we find significant departures for the eigenfunctions.

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.

THE TEMPERATURE DISTRIBUTION PRODUCED BY ACOUSTIC ABSORPTION: I. MACROSCOPIC TREATMENT

1966 ◽  
Vol 44 (12) ◽  
pp. 3001-3011 ◽  
Author(s):  
S. Simons
Keyword(s):  
Temperature Distribution ◽  
Acoustic Wave ◽  
Numerical Results ◽  
Time Dependent ◽  
Acoustic Absorption ◽  
Space And Time

A calculation is given of the temperature distribution in space and time produced by the absorption of an acoustic wave propagated inside a medium, under conditions in which the situation may be described macroscopically. The problem is considered for various geometries, and for both constant and time-dependent energies of the incident acoustic wave. Numerical results are obtained, and a discussion is given of their relevance to various experiments.

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
Sign in / Sign up

Export Citation Format

Share Document