Related Experiment Video
Updated: Jul 15, 2026

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry
Published on: April 8, 2020
Accurate numerical solutions of the time-dependent Schrödinger equation
1Physics Department, Redeemer University College, Ancaster, Ontario L9K 1J4, Canada. vandijk@physics.mcmaster.ca
Abstract:
We present a generalization of the often-used Crank-Nicolson (CN) method of obtaining numerical solutions of the time-dependent Schrödinger equation. The generalization yields numerical solutions accurate to order (Deltax)2r-1 in space and (Deltat)2M in time for any positive integers r and M, while CN employ r=M=1. We note dramatic improvement in the attainable precision (circa ten or greater orders of magnitude) along with several orders of magnitude reduction of computational time. The improved method is shown to lead to feasible studies of coherent-state oscillations with additional short-range interactions, wave-packet scattering, and long-time studies of decaying systems.
More Related Videos
08:04Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids
Published on: May 27, 2020
11:03An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
Related Concept Videos
The Quantum-Mechanical Model of an Atom
Linear Approximation in Time Domain
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length, the...
Electron Orbital Model
The de Broglie Wavelength
Kinematic Equations: Problem Solving
The Uncertainty Principle