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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...
The Uncertainty Principle04:08

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Werner Heisenberg considered the limits of how accurately one can measure properties of an electron or other microscopic particles. He determined that there is a fundamental limit to how accurately one can measure both a particle’s position and its momentum simultaneously. The more accurate the measurement of the momentum of a particle is known, the less accurate the position at that time is known and vice versa. This is what is now called the Heisenberg uncertainty principle. He mathematically...
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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...
¹H NMR: Interpreting Distorted and Overlapping Signals01:02

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Spin systems where the difference in chemical shifts of the coupled nuclei is greater than ten times J are called first-order spin systems. These nuclei are weakly coupled, and their chemical shifts and coupling constant can generally be estimated from the well-separated signals in the spectrum.
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Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids
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Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids

Published on: May 27, 2020

Numerically exact quantum dynamics for indistinguishable particles: the multilayer multiconfiguration time-dependent

Haobin Wang1, Michael Thoss

  • 1Department of Chemistry and Biochemistry, New Mexico State University, MSC 3C, Las Cruces, New Mexico 88003, USA. whb@intrepid.nmsu.edu

The Journal of Chemical Physics
|July 17, 2009
PubMed
Summary

A novel quantum dynamics theory simulates identical particles using second quantization and Fock space decomposition. This approach unifies methods for distinguishable and indistinguishable particles, including fermions and bosons.

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Generation and Coherent Control of Pulsed Quantum Frequency Combs
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Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

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Last Updated: Jun 21, 2026

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids
08:04

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids

Published on: May 27, 2020

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

Area of Science:

  • Quantum mechanics
  • Many-body quantum theory
  • Computational physics

Background:

  • Simulating quantum dynamics in systems of identical particles presents significant theoretical challenges.
  • Existing methods often struggle to unify the treatment of distinguishable and indistinguishable particles.

Purpose of the Study:

  • To propose a new, accurate theory for simulating quantum dynamics in systems of identical particles.
  • To unify existing theoretical frameworks for both distinguishable and indistinguishable particles.

Main Methods:

  • The theory is based on the second quantization formalism and Fock space representation using occupation-number states.
  • It decomposes the Fock space into smaller subspaces, enabling a multilayer multiconfiguration Hartree expansion.
  • Specific formulations are developed for fermions, bosons, and their combinations, including operator algebra for particle symmetry.

Main Results:

  • A unified theoretical framework is presented for simulating quantum dynamics across various particle types.
  • The method allows for the expression of wave functions using multilayer multiconfiguration Hartree expansions.
  • Numerical illustration on vibrationally coupled electron transport demonstrates the theory's applicability.

Conclusions:

  • The proposed theory offers an accurate and unified approach to simulating quantum dynamics in systems of identical particles.
  • It provides a flexible framework adaptable to different particle statistics (fermions, bosons).
  • The method is computationally practical and validated through a relevant numerical example.