Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

The Quantum-Mechanical Model of an Atom

The Quantum-Mechanical Model of an Atom

Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, Erwin Schrödinger extended de Broglie’s work by deriving what is now known as the Schrödinger equation. When Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing hydrogen spectra. Schrödinger...

The de Broglie Wavelength

The de Broglie Wavelength

In the macroscopic world, objects that are large enough to be seen by the naked eye follow the rules of classical physics. A billiard ball moving on a table will behave like a particle; it will continue traveling in a straight line unless it collides with another ball, or it is acted on by some other force, such as friction. The ball has a well-defined position and velocity or well-defined momentum, p = mv, which is defined by mass m and velocity v at any given moment. This is the typical...

Graphing the Wave Function

Graphing the Wave Function

Consider the wave equation for a sinusoidal wave moving in the positive x-direction. The wave equation is a function of both position and time. From the wave equation, two different graphs can be plotted.

Equations of Wave Motion

Equations of Wave Motion

Mathematically, the motion of a wave can be studied using a wavefunction. Consider a string oscillating up and down in simple harmonic motion, having a period T. The wave on the string is sinusoidal and is translated in the positive x-direction as time progresses. Sine is a function of the angle θ, oscillating between +A and −A and repeating every 2π radians. To construct a wave model, the ratio of the angle θ and the position x is considered.

The Bohr Model

The Bohr Model

Following the work of Ernest Rutherford and his colleagues in the early twentieth century, the picture of atoms consisting of tiny dense nuclei surrounded by lighter and even tinier electrons continually moving about the nucleus was well established. This picture was called the planetary model since it pictured the atom as a miniature “solar system” with the electrons orbiting the nucleus like planets orbiting the sun. The simplest atom is hydrogen, consisting of a single proton as the nucleus...

Plane Electromagnetic Waves I

Plane Electromagnetic Waves I

The existence of combined electric and magnetic fields that propagate through space as electromagnetic (EM) waves is the most significant prediction of Maxwell's equations. As Maxwell's equations hold in free space, the predicted electromagnetic waves do not require a medium for their propagation. An EM wave comprises an electric field, defined as the force per charge on a stationary charge, and a magnetic field, which is the force per charge on a moving charge.
The EM field is assumed to be a...

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by

Same author

Development of Parallel On-the-Fly <i>Crystal</i> Algorithm for Reaction Discovery in Large and Complex Molecular Systems.

Journal of chemical theory and computation·2025

Same author

Development of Parallel On-the-Fly <b></b> Algorithm for Global Exploration of Conical Intersection Seam Space.

Journal of chemical theory and computation·2024

Same author

Dwell Times, Wavepacket Dynamics, and Quantum Trajectories for Particles with Spin 1/2.

Entropy (Basel, Switzerland)·2024

Same author

"On-the-fly" <math></math> : How to reliably and automatically characterize and construct potential energy surfaces.

Journal of computational chemistry·2024

Same author

Quantum Dynamical Investigation of Dihydrogen-Hydride Exchange in a Transition-Metal Polyhydride Complex.

The journal of physical chemistry. A·2023

Same author

Adiabatic and Nonadiabatic Dynamics with Interacting Quantum Trajectories.

Journal of chemical theory and computation·2022

Search research articles

Related Experiment Video

Updated: Jun 27, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Quantum trajectory calculations for bipolar wavepacket dynamics in one dimension.

Kisam Park¹, Bill Poirier, Gérard Parlant

¹Department of Chemistry and Biochemistry, Texas Tech University, P.O. Box 41061, Lubbock, Texas 79409-1061, USA. kisam.park@ttu.edu

The Journal of Chemical Physics

|November 26, 2008

Summary

This summary is machine-generated.

Quantum trajectory methods (QTMs) overcome the "node problem" using a bipolar decomposition. This approach enables accurate quantum dynamics simulations, even for complex systems with wavepacket interference.

More Related Videos

Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform

Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform

Published on: August 2, 2019

Related Experiment Videos

Last Updated: Jun 27, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform

Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform

Published on: August 2, 2019

Area of Science:

Quantum mechanics
Computational chemistry
Theoretical physics

Background:

Quantum trajectory methods (QTMs) offer a path to exact quantum dynamics with computational efficiency.
The "node problem," caused by wavepacket interference, hinders QTM development and numerical stability.
Previous work introduced a "bipolar decomposition" to manage oscillatory wavepacket densities.

Purpose of the Study:

To implement and validate the bipolar decomposition within a quantum trajectory method framework.
To assess the accuracy of the bipolar QTM for systems with significant wavepacket interference.
To explore the implications of the bipolar QTM for classical limits and multidimensional systems.

Main Methods:

Applied a "bipolar decomposition" (psi=psi+(+)(psi)psi(-)) to one-dimensional wavepacket dynamics.
Utilized quantum trajectory methods (QTMs) with the bipolar approach to simulate quantum dynamics.
Tested the method on two benchmark 1D systems with substantial interference, including a more classical-like system.

Main Results:

The bipolar decomposition successfully generated interference-free component densities, even for oscillatory wavepackets.
Quantum trajectory method simulations using the bipolar approach yielded highly accurate results for a challenging, classical-like system.
The accuracy was validated against a fixed-grid calculation.

Conclusions:

The bipolar decomposition is well-suited for quantum trajectory methods, effectively addressing the node problem.
This approach enables accurate quantum dynamics simulations for systems with significant wavepacket interference.
The bipolar QTM shows promise for studying the classical limit and for future multidimensional applications.