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Related Concept Videos

Adiabatic Processes for an Ideal Gas01:18

Adiabatic Processes for an Ideal Gas

When an ideal gas is compressed adiabatically, that is, without adding heat, work is done on it, and its temperature increases. In an adiabatic expansion, the gas does work, and its temperature drops. Adiabatic compressions actually occur in the cylinders of a car, where the compressions of the gas-air mixture take place so quickly that there is no time for the mixture to exchange heat with its environment. Nevertheless, because work is done on the mixture during the compression, its...
Linear Differential Equations01:27

Linear Differential Equations

The integrating factor method provides a systematic way to solve first-order linear differential equations, especially those that cannot be handled by separation of variables. This method is particularly useful in modeling time-dependent physical systems influenced by both constant inputs and resistive forces. A common example is the motion of a car subjected to a constant engine force while experiencing air resistance proportional to its velocity.In such scenarios, Newton’s second law yields a...
Euler Equations of Motion01:19

Euler Equations of Motion

Imagine a rigid body that is rotating at an angular velocity of ω within an inertial frame of reference. Along with this, picture a second rotating frame that is attached to the body itself. This frame moves along with the body and possesses an angular velocity of Ω. The total moment about the center of mass is calculated by adding the rate of change of angular momentum about the center of mass in relation to the rotating frame and the cross-product of the body's angular velocity and its...
Conservation of Mass in Moving, Nondeforming Control Volume01:14

Conservation of Mass in Moving, Nondeforming Control Volume

Stormwater detention basins are essential in managing runoff during heavy rainfall, particularly in urban areas where impervious surfaces increase the risk of flooding. Understanding the conservation of mass in these systems allows engineers to optimize basin performance, balancing inflow, outflow, and water storage.
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Pressure and Volume in an Adiabatic Process01:27

Pressure and Volume in an Adiabatic Process

Free expansion of a gas is an adiabatic process. However, there are few differences between free expansion and adiabatic expansion. During free expansion, no work is done, and there is no change in internal energy. But, for an adiabatic expansion, work is done, and there is a change in internal energy. During an adiabatic process, the relation between the pressure and volume is obtained from the condition for the adiabatic process, that is,
Equation of Motion: General Plane motion - Problem Solving01:16

Equation of Motion: General Plane motion - Problem Solving

Consider a lawn roller with a mass of 100 kg, a radius of 0.2 meters, and a radius of gyration of 0.15 meters. A force of 200 N is applied to this roller, angled at 60 degrees from the horizontal plane. What will be the angular acceleration of the lawn roller?
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Related Experiment Video

Updated: May 25, 2026

Multiscale Sampling of a Heterogeneous Water/Metal Catalyst Interface using Density Functional Theory and Force-Field Molecular Dynamics
10:52

Multiscale Sampling of a Heterogeneous Water/Metal Catalyst Interface using Density Functional Theory and Force-Field Molecular Dynamics

Published on: April 12, 2019

Constrained adiabatic trajectory method: a global integrator for explicitly time-dependent Hamiltonians.

A Leclerc1, G Jolicard, D Viennot

  • 1Institut UTINAM, CNRS UMR 6213, Université de Franche-Comté, Observatoire de Besançon, 41 bis Avenue de l'Observatoire, BP 1615, 25010 Besançon Cedex, France. Arnaud.Leclerc@utinam.cnrs.fr

The Journal of Chemical Physics
|January 14, 2012
PubMed
Summary
This summary is machine-generated.

The constrained adiabatic trajectory method (CATM) offers a novel approach for solving the Schrödinger equation, particularly for complex systems. This method enhances Hamiltonian spectrum analysis and handles intricate time-dependent interactions effectively.

Related Experiment Videos

Last Updated: May 25, 2026

Multiscale Sampling of a Heterogeneous Water/Metal Catalyst Interface using Density Functional Theory and Force-Field Molecular Dynamics
10:52

Multiscale Sampling of a Heterogeneous Water/Metal Catalyst Interface using Density Functional Theory and Force-Field Molecular Dynamics

Published on: April 12, 2019

Area of Science:

  • Quantum mechanics
  • Computational chemistry
  • Theoretical physics

Background:

  • The Schrödinger equation is central to quantum mechanics.
  • Various numerical methods exist for integrating the Schrödinger equation.
  • Adiabatic processes are crucial in understanding quantum system dynamics.

Purpose of the Study:

  • To reexamine the constrained adiabatic trajectory method (CATM) as a Schrödinger equation integrator.
  • To analyze the CATM's performance for adiabatic processes and complex time-dependencies.
  • To illustrate the CATM's capabilities with a numerical example of the H(2)(+) ion.

Main Methods:

  • Reexamination of the constrained adiabatic trajectory method (CATM).
  • Contextualization of CATM within existing literature on Schrödinger equation integrators.
  • Detailed analysis of the interdependence between CATM, wave operator, Floquet, and (t, t') theories.
  • Numerical calculation involving the H(2)(+) ion under a laser pulse.

Main Results:

  • The CATM can effectively dilate the Hamiltonian spectrum, enabling perturbative treatments.
  • The method demonstrates the capacity to handle highly complex time-dependencies in quantum systems.
  • Numerical results for the H(2)(+) ion validate the CATM's applicability.

Conclusions:

  • The constrained adiabatic trajectory method (CATM) is a robust integrator for the Schrödinger equation.
  • CATM facilitates perturbative approaches by modifying the Hamiltonian spectrum.
  • The method excels in managing intricate time-dependent interactions in quantum dynamics.