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The Bohr Model

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Following the work of Ernest Rutherford and his colleagues in the early twentieth century, the picture of atoms consisting of tiny dense nuclei surrounded by lighter and even tinier electrons continually moving about the nucleus was well established. This picture was called the planetary model since it pictured the atom as a miniature “solar system” with the electrons orbiting the nucleus like planets orbiting the sun. The simplest atom is hydrogen, consisting of a single proton as the nucleus...

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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...

Electron Orbital Model

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Related Experiment Video

Updated: Jul 3, 2026

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

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

Published on: May 27, 2020

One-dimensional extended Hubbard model in the atomic limit.

F Mancini¹, F P Mancini

¹Dipartimento di Fisica E R Caianiello, Unità CNISM di Salerno, Università degli Studi di Salerno, Via S Allende, Baronissi SA, Italy.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|July 23, 2008

Summary

This summary is machine-generated.

This study provides an exact solution for the one-dimensional extended Hubbard model, identifying four distinct phases and charge ordering behaviors at zero temperature. Finite temperatures reveal persistent order and excitations linked to charge density redistribution.

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Last Updated: Jul 3, 2026

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

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Published on: May 27, 2020

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Probe Type II Band Alignment in One-Dimensional Van Der Waals Heterostructures Using First-Principles Calculations

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Published on: October 12, 2019

Area of Science:

Condensed Matter Physics
Quantum Many-Body Systems

Background:

The extended Hubbard model is crucial for understanding correlated electron systems.
Atomic limit simplifies complex models for analytical solutions.

Purpose of the Study:

To provide an exact solution for the 1D extended Hubbard model in the atomic limit.
To systematically analyze its properties across the entire parameter space.
To identify phases, transitions, and excitations.

Main Methods:

Green's function formalism
Equations of motion formalism
Analysis of response and correlation functions
Thermodynamic quantities investigation

Main Results:

Identification of four distinct phases and charge ordering at T=0 in the (U,n) plane.
Evidence of persistent finite-range order at finite temperatures.
Exact determination of elementary excitations and density of states.
Two-peak structure in charge susceptibility and entropy linked to charge density redistribution.

Conclusions:

The exact solution reveals rich phase behavior and ordering in the 1D extended Hubbard model.
Finite-temperature properties indicate robust correlations and excitations.
The study clarifies the relationship between specific heat, excitations, and charge density.