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Related Concept Videos

Classical Mechanics01:12

Classical Mechanics

Classical mechanics provides a mathematical description of the motion of bodies under the influence of forces. A key principle within this field is the work-energy theorem, which establishes a bridge between the net work done on an object and its kinetic energy.The work-energy theorem states that the net work done on a particle by all the forces acting on it equals the change in its kinetic energy.In simple terms, the work-energy theorem is a method to analyze the effects of forces on an...
The Quantum-Mechanical Model of an Atom02:45

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...
An Introduction to Mechanics01:28

An Introduction to Mechanics

Humans have been making ships, shelters, pyramids, weapons, agricultural equipment, and many more items without recording the process or theory behind them for centuries. It would be challenging to document the evolution of mechanics from its origin to the present.
According to records, the history of mechanics starts with Aristotle (384–322 BC). He related mechanics to physical theory, aiming for a universal synthesis.
Newton defined mechanics as the branch of physical science that studies the...
The de Broglie Wavelength02:32

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...
Mechanistic Models: Overview of Compartment Models01:21

Mechanistic Models: Overview of Compartment Models

Mechanistic models, a category encompassing both physiological and compartmental modeling, differ from empirical models' approaches to incorporating known factors about the systems being modeled. Empirical models describe data with minimal assumptions, while mechanistic models aim to provide a robust description of available data by specifying assumptions and integrating known factors about the system. Compartmental analysis is a key example of a mechanistic model in pharmacokinetics and...
One-Degree-of-Freedom System01:24

One-Degree-of-Freedom System

In mechanical engineering, one-degree-of-freedom systems form the basis of a wide range of electrical and mechanical components. Using these models, engineers can predict the behavior of various parts in a larger system, which gives them insight into how different forces interact with each other.
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Related Experiment Video

Updated: May 16, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs
06:42

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Operational dynamic modeling transcending quantum and classical mechanics.

Denys I Bondar1, Renan Cabrera, Robert R Lompay

  • 1Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA. dbondar@princeton.edu

Physical Review Letters
|December 11, 2012
PubMed
Summary
This summary is machine-generated.

We present a new framework for operational dynamic modeling (ODM) that unifies classical and quantum mechanics. This approach combines kinematics with the evolution of dynamical averages, enabling new theoretical formulations.

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Area of Science:

  • Theoretical physics
  • Mathematical physics

Background:

  • Existing dynamic modeling approaches often lack a unified framework.
  • Bridging classical and quantum mechanics in a single model is a persistent challenge.

Purpose of the Study:

  • To introduce a general and systematic theoretical framework for operational dynamic modeling (ODM).
  • To demonstrate the framework's capability to encompass diverse physical dynamics.

Main Methods:

  • Combining a kinematic description with the evolution of dynamical average values.
  • Utilizing the algebra of observables and their averages.
  • Employing Ehrenfest-like theorems for the evolution of average values.

Main Results:

  • Operational Dynamic Modeling (ODM) provides a unified approach.
  • The framework successfully integrates classical non-relativistic mechanics and quantum field theory.
  • ODM offers a basis for developing novel physical theories.

Conclusions:

  • The proposed operational dynamic modeling framework is broadly applicable across physics.
  • ODM facilitates the formulation of new theories by providing a systematic foundation.