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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.

Quantum Numbers

Quantum Numbers

It is said that the energy of an electron in an atom is quantized; that is, it can be equal only to certain specific values and can jump from one energy level to another but not transition smoothly or stay between these levels.

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An atomic orbital represents the three-dimensional regions in an atom where an electron has the highest probability to reside. The radial distribution function indicates the total probability of finding an electron within the thin shell at a distance r from the nucleus. The atomic orbitals have distinct shapes which are determined by l, the angular momentum quantum number. The orbitals are often drawn with a boundary surface, enclosing densest regions of the cloud.

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The elements in groups of the periodic table exhibit similar chemical behavior. This similarity occurs because the members of a group have the same number and distribution of electrons in their valence shells.

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Hybridization of Atomic Orbitals I

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The mathematical expression known as the wave function, ψ, contains information about each orbital and the wavelike properties of electrons in an isolated atom. When atoms are bound together in a molecule, the wave functions combine to produce new mathematical descriptions that have different shapes. This process of combining the wave functions for atomic orbitals is called hybridization and is mathematically accomplished by the linear combination of atomic orbitals. The new orbitals that...

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Related Experiment Video

Updated: Feb 8, 2026

Gradient Echo Quantum Memory in Warm Atomic Vapor

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Published on: November 11, 2013

Quantum Many-Body Dynamics for Fermionic t-J Model Simulated with Atom Arrays.

Ye-Bing Zhang^1,2, Xin-Chi Zhou^1,2, Bao-Zong Wang^1,2

¹Peking University, International Center for Quantum Materials and School of Physics, Beijing 100871, China.

Physical Review Letters

|February 6, 2026

Summary

Researchers developed a new method to simulate the fermionic t-J model using Rydberg-dressed atoms. This approach reveals a novel self-pinning effect in quantum many-body dynamics, offering insights into high-temperature superconductivity.

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Area of Science:

Quantum Simulation
Condensed Matter Physics
Atomic Physics

Background:

The fermionic t-J model is crucial for understanding strongly correlated systems, especially high-temperature superconductors.
Simulating this model presents significant challenges for current quantum platforms.
Exploring high-temperature superconductivity requires advanced simulation techniques.

Purpose of the Study:

To propose a novel scheme for realizing a highly tunable extended t-J model.
To investigate quantum many-body dynamics in the large J/t limit.
To explore exotic quantum phenomena beyond conventional systems.

Main Methods:

Utilizing a programmable Rydberg-dressed tweezer array.
Engineering Rydberg-dressed dipole-dipole interactions and inter-tweezer couplings.
Achieving independently tunable exchange (J) and hopping (t) couplings.

Main Results:

Successfully realized a tunable fermionic t-J model.
Predicted an unprecedented many-body self-pinning effect in the large J/t regime.
Observed novel nonthermal quantum many-body dynamics violating the eigenstate thermalization hypothesis.

Conclusions:

The proposed scheme opens new avenues for exploring exotic quantum many-body physics with the t-J model.
This work represents a significant step towards simulating high-temperature superconductivity in neutral atom systems.
The predicted self-pinning effect offers a new paradigm for understanding quantum dynamics.