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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...
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Related Experiment Video

Updated: May 24, 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

Approach to typicality in many-body quantum systems.

Shawn Dubey1, Luciano Silvestri, Justin Finn

  • 1Department of Physics, University of Massachusetts at Boston, 100 Morrissey Boulevard, Boston, Massachusetts 02125, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|March 10, 2012
PubMed
Summary

Many-body lattice systems approach thermal equilibrium as subsystem count increases, supporting the eigenstate thermalization hypothesis. Deviations from typicality decrease exponentially with system size.

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Last Updated: May 24, 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

Area of Science:

  • Quantum statistical mechanics
  • Condensed matter physics
  • Many-body systems

Background:

  • The eigenstate thermalization hypothesis (ETH) explains thermalization in quantum systems.
  • Typical Hamiltonians in large Hilbert spaces lead to thermal equilibrium in small subsystems.
  • Understanding the emergence of thermalization in complex quantum systems is crucial.

Purpose of the Study:

  • To provide numerical evidence for the eigenstate thermalization hypothesis in many-body lattice systems.
  • To investigate how systems approach typicality as the number of subsystems increases.
  • To characterize the deviation from typicality as a function of system size and Hilbert space dimension.

Main Methods:

  • Numerical simulations of many-body lattice systems.
  • Analysis of system typicality and deviation from equilibrium.
  • Averaging over random nearest-neighbor interactions.

Main Results:

  • Many-body lattice systems generically approach typicality with increasing subsystem count.
  • Deviation from typicality decreases exponentially with the number of subsystems.
  • Averaging over random interactions yields a power-law for atypicality, distinct from random Hamiltonians.

Conclusions:

  • Numerical results support the eigenstate thermalization hypothesis in many-body lattice systems.
  • System size plays a critical role in the exponential suppression of deviations from thermal equilibrium.
  • The study reveals unique scaling properties of atypicality in specific lattice models.