Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

State Space Representation01:27

State Space Representation

251
The frequency-domain technique, commonly used in analyzing and designing feedback control systems, is effective for linear, time-invariant systems. However, it falls short when dealing with nonlinear, time-varying, and multiple-input multiple-output systems. The time-domain or state-space approach addresses these limitations by utilizing state variables to construct simultaneous, first-order differential equations, known as state equations, for an nth-order system.
Consider an RLC circuit, a...
251
Differential Form of Maxwell's Equations01:17

Differential Form of Maxwell's Equations

552
James Clerk Maxwell (1831–1879) was one of the significant contributors to physics in the nineteenth century. He is probably best known for having combined existing knowledge of the laws of electricity and the laws of magnetism with his insights to form a complete overarching electromagnetic theory, represented by Maxwell's equations. The four basic laws of electricity and magnetism were discovered experimentally through the work of physicists such as Oersted, Coulomb, Gauss, and...
552
Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

110
Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
110
Signal Flow Graphs01:18

Signal Flow Graphs

277
Signal-flow graphs offer a streamlined and intuitive approach to representing control systems, providing an alternative to traditional block diagrams. These graphs use branches to symbolize systems and nodes to represent signals, effectively illustrating the relationships and interactions within the system.
In a signal-flow graph, branches denote the system's transfer functions, while nodes represent the signals. The direction of signal flow is indicated by arrows, with the corresponding...
277
Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

120
Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....
120
Transfer Function to State Space01:23

Transfer Function to State Space

337
State-space representation is a powerful tool for simulating physical systems on digital computers, necessitating the conversion of the transfer function into state-space form. Consider an nth-order linear differential equation with constant coefficients, like those encountered in an RLC circuit. The state variables are selected as the output and its n−1 derivatives. Differentiating these variables and substituting them back into the original equation produces the state equations.
In an...
337

You might also read

Related Articles

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

Sort by
Same author

Combining classical reactive scattering and the time-energy uncertainty relation.

Physical chemistry chemical physics : PCCP·2026
Same author

Classical dynamics in a quantum spirit: Refining semi-classical corrections for the scattering of H2 on W(100).

The Journal of chemical physics·2025
Same author

A practical quasi-classical trajectory method to avoid zero-point energy leakage in dissociative chemisorption of polyatomic molecules on surfaces.

The Journal of chemical physics·2025
Same author

The Experimental Rate Constant of the <i>S</i> <sup>+</sup>(<sup>2</sup> <i>D</i>) + <i>H</i> <sub>2</sub> Reaction.

ACS earth & space chemistry·2025
Same author

A quasi-classical study in a quantum spirit of mode specificity of the H + HOD abstraction reaction.

Physical chemistry chemical physics : PCCP·2024
Same author

How Adsorbed Oxygen Atoms Inhibit Hydrogen Dissociation on Tungsten Surfaces.

The journal of physical chemistry letters·2023

Related Experiment Video

Updated: Aug 6, 2025

Interactive and Visualized Online Experimentation System for Engineering Education and Research
08:35

Interactive and Visualized Online Experimentation System for Engineering Education and Research

Published on: November 24, 2021

2.5K

Semiclassical initial value representation: From Møller to Miller. II.

Laurent Bonnet1

  • 1Univ. Bordeaux, CNRS, Bordeaux INP, ISM, UMR 5255, F-33400 Talence, France.

The Journal of Chemical Physics
|March 22, 2023
PubMed
Summary
This summary is machine-generated.

This study demonstrates that semiclassical theory using shifted angles accurately describes inelastic molecular collisions. It confirms Miller's semiclassical initial value representation (SCIVR) and enhances scattering calculations for long-range forces.

More Related Videos

MPI CyberMotion Simulator: Implementation of a Novel Motion Simulator to Investigate Multisensory Path Integration in Three Dimensions
09:46

MPI CyberMotion Simulator: Implementation of a Novel Motion Simulator to Investigate Multisensory Path Integration in Three Dimensions

Published on: May 10, 2012

12.7K
Quantifying Mixing using Magnetic Resonance Imaging
07:33

Quantifying Mixing using Magnetic Resonance Imaging

Published on: January 25, 2012

11.0K

Related Experiment Videos

Last Updated: Aug 6, 2025

Interactive and Visualized Online Experimentation System for Engineering Education and Research
08:35

Interactive and Visualized Online Experimentation System for Engineering Education and Research

Published on: November 24, 2021

2.5K
MPI CyberMotion Simulator: Implementation of a Novel Motion Simulator to Investigate Multisensory Path Integration in Three Dimensions
09:46

MPI CyberMotion Simulator: Implementation of a Novel Motion Simulator to Investigate Multisensory Path Integration in Three Dimensions

Published on: May 10, 2012

12.7K
Quantifying Mixing using Magnetic Resonance Imaging
07:33

Quantifying Mixing using Magnetic Resonance Imaging

Published on: January 25, 2012

11.0K

Area of Science:

  • * Quantum Chemistry and Molecular Dynamics
  • * Theoretical Chemistry
  • * Chemical Physics

Background:

  • * Semiclassical (SC) theory offers a powerful approach to molecular scattering.
  • * Miller's seminal work established the initial value representation (IVR) using shifted angles as a convenient and accurate SC method.
  • * Standard treatments often employ natural angles, differing from the shifted angles crucial for SCIVR.

Purpose of the Study:

  • * To demonstrate the equivalence of shifted angle classical paths in SCIVR to those in Tannor-Weeks quantum scattering theory.
  • * To confirm the underlying role of Møller operators in Miller's SC formulation for molecular collisions.
  • * To improve the accuracy and ease of the Skinner-Miller method for long-range anisotropic forces using shifted coordinates.

Main Methods:

  • * Application of Miller's semiclassical initial value representation (SCIVR) with shifted angles.
  • * Utilizing van Vleck propagators and stationary phase approximation.
  • * Connecting SCIVR to Tannor-Weeks quantum scattering theory and Møller operators.

Main Results:

  • * Shifted angles define classical paths identical to those in the classical limit of Tannor-Weeks theory when specific wave packets are used.
  • * Miller's SCIVR expression for S-matrix elements is recovered, including a cut-off factor for energetically forbidden transitions.
  • * Møller operators are confirmed to underlie Miller's SC formulation for molecular collisions.
  • * The Skinner-Miller method in shifted coordinates shows improved accuracy and ease for long-range anisotropic forces.

Conclusions:

  • * The study validates Miller's SCIVR approach by linking it to established quantum scattering theories.
  • * The findings confirm the theoretical underpinnings of SCIVR and its connection to Møller operators.
  • * Shifted coordinates offer a more effective framework for applying methods like Skinner-Miller, particularly for systems with long-range interactions.