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Related Concept Videos

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...
Van der Waals Equation01:10

Van der Waals Equation

The ideal gas law is an approximation that works well at high temperatures and low pressures. The van der Waals equation of state (named after the Dutch physicist Johannes van der Waals, 1837−1923) improves it by considering two factors.
First, the attractive forces between molecules, which are stronger at higher densities and reduce the pressure, are considered by adding to the pressure a term equal to the square of the molar density multiplied by a positive coefficient a. Second, the volume...
The Van der Waals Equation01:26

The Van der Waals Equation

The ideal gas law is based on two simplifying assumptions: first, that there are no intermolecular attractions between gas molecules, and second, that the volume occupied by the molecules themselves is negligible compared with the volume of the container. However, these assumptions don't hold up under all conditions - specifically, at high pressures and low temperatures, as gas tends to deviate from ideal gas behavior.The van der Waals equation is an enhanced version of the ideal gas law,...
Ideal Gas Equation01:17

Ideal Gas Equation

The ideal gas equation is an equation of state that relates the state variables pressure, volume, temperature, and the number of moles of a hypothetical gas. This equation is a combination of four empirical laws, namely Boyle’s Law, Charles’s Law, Avogadro’s Law, and Gay-Lussac’s Law. When the proportionalities of the above four empirical laws are combined, it results in a single proportionality constant known as the universal gas constant.
Maxwell-Boltzmann Distribution: Problem Solving01:20

Maxwell-Boltzmann Distribution: Problem Solving

Individual molecules in a gas move in random directions, but a gas containing numerous molecules has a predictable distribution of molecular speeds, which is known as the Maxwell-Boltzmann distribution, f(v).
This distribution function f(v) is defined by saying that the expected number N (v1,v2) of particles with speeds between v1 and v2 is given by
Real Gases: Effects of Intermolecular Forces and Molecular Volume Deriving Van der Waals Equation04:01

Real Gases: Effects of Intermolecular Forces and Molecular Volume Deriving Van der Waals Equation

Thus far, the ideal gas law, PV = nRT, has been applied to a variety of different types of problems, ranging from reaction stoichiometry and empirical and molecular formula problems to determining the density and molar mass of a gas. However, the behavior of a gas is often non-ideal, meaning that the observed relationships between its pressure, volume, and temperature are not accurately described by the gas laws.

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Related Experiment Video

Updated: Jul 19, 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

Master equation for a quantum particle in a gas.

Klaus Hornberger1

  • 1Arnold Sommerfeld Center for Theoretical Physics, Ludwig-Maximilians-Universität München, Theresienstrasse 37, 80333 Munich, Germany. www.klaus-hornberger.de

Physical Review Letters
|October 10, 2006
PubMed
Summary

A new quantum equation describes Brownian particle motion in gases, unifying quantum scattering, decoherence, and dissipation. This quantum Boltzmann equation advances understanding of quantum systems interacting with their environment.

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An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
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An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

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Last Updated: Jul 19, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs
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An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
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An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

Area of Science:

  • Quantum mechanics
  • Statistical mechanics
  • Chemical physics

Background:

  • Brownian motion describes particle movement in a fluid.
  • Quantum effects become significant at microscopic scales.
  • Understanding quantum dissipation and decoherence is crucial.

Purpose of the Study:

  • Derive a quantum mechanical equation for Brownian particle motion.
  • Develop a unified framework for quantum scattering, decoherence, and dissipation.
  • Incorporate quantum effects into the linear Boltzmann equation.

Main Methods:

  • Utilized S-matrix theory to derive the quantum equation.
  • Developed a quantum version of the linear Boltzmann equation.
  • Formulated a completely positive master equation.

Main Results:

  • The derived equation nonperturbatively accounts for quantum scattering effects.
  • The framework unifies the description of decoherence and dissipation.
  • The equation reduces to known limits for specific cases.

Conclusions:

  • The quantum linear Boltzmann equation provides a comprehensive description of quantum Brownian motion.
  • This work offers a unified approach to quantum dissipation and decoherence.
  • The derived master equation serves as a valuable tool in quantum statistical mechanics.