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The Quantum-Mechanical Model of an Atom

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.

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If in an experiment, data values have a probability of being both positive and negative, neither the arithmetic mean, the geometric mean, nor the harmonic mean can be used to calculate the central tendency of the data set. In particular, if the positive and negative values are equally likely, the arithmetic mean is close to zero.
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Related Experiment Video

Updated: Jan 20, 2026

The Quantum-Mechanical Model of an Atom

The Quantum-Mechanical Model of an Atom

Exactly Solvable Quantum Impurity Model with Inverse-Square Interactions.

Hong-Hao Tu¹, Ying-Hai Wu²

¹Institut für Theoretische Physik, Technische Universität Dresden, 01062 Dresden, Germany.

Physical Review Letters

|September 7, 2019

Summary

This summary is machine-generated.

We developed an exactly solvable quantum impurity model for spin-1/2 Kondo physics. This model features unique ground states and Hamiltonians, offering new insights into quantum magnetism.

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Published on: April 30, 2023

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Last Updated: Jan 20, 2026

The Quantum-Mechanical Model of an Atom

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Glovebox-Operating Procedure and Use of Impurity Sensors

Glovebox-Operating Procedure and Use of Impurity Sensors

Published on: April 30, 2023

Area of Science:

Condensed Matter Physics
Quantum Many-Body Theory

Background:

The Kondo effect describes the interaction between magnetic impurities and conduction electrons in metals.
Developing exactly solvable models is crucial for understanding complex quantum phenomena like the Kondo effect.

Purpose of the Study:

To construct a novel, exactly solvable quantum impurity model.
To investigate the fundamental properties of spin-1/2 Kondo physics.

Main Methods:

Construction of a quantum impurity model with spin-1/2 conduction fermions and a spin-1/2 magnetic moment.
Utilizing a Gutzwiller projected Fermi sea with nonorthonormal modes for the ground state.
Defining a parent Hamiltonian with all-to-all inverse-square hopping and spin-exchange terms.

Main Results:

The model's ground state is a Jastrow-type homogeneous polynomial in the site-occupation basis.
Analysis of low-lying energy levels, spin-spin correlation function, and entanglement entropy confirms Kondo physics.
Demonstrated the model's capacity to generate other exactly solvable quantum impurity models.

Conclusions:

The constructed model successfully captures essential aspects of spin-1/2 Kondo physics.
The developed methodology provides a framework for creating new exactly solvable quantum impurity models.
This work advances the theoretical understanding of quantum impurity systems and Kondo physics.