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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.

Fermi Level Dynamics

Fermi Level Dynamics

The vacuum level denotes the energy threshold required for an electron to escape from a material surface. It is usually positioned above the conduction band of a semiconductor and acts as a benchmark for comparing electron energies within various materials.
Electron affinity in semiconductors refers to the energy gap between the minimum of its conduction band and the vacuum level and it is a critical parameter in determining how easily a semiconductor can accept additional electrons.
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Equilibrium Conditions for a Particle

Equilibrium Conditions for a Particle

When an object is in equilibrium, it is either at rest or moving with a constant velocity. There are two types of equilibrium: static and dynamic. Static equilibrium occurs when an object is at rest, while dynamic equilibrium occurs when an object is moving with a constant velocity. In both cases, there must be a balance of forces acting on the object.
To understand the concept of equilibrium, let us first consider the forces acting on an object. When different forces act on an object, they can...

First Law: Particles in One-dimensional Equilibrium

First Law: Particles in One-dimensional Equilibrium

Newton's first law of motion states that a body at rest remains at rest, or if in motion, remains in motion at constant velocity, unless acted on by a net external force. It also states that there must be a cause for any change in velocity (a change in either magnitude or direction) to occur. This cause is a net external force. For example, consider what happens to an object sliding along a rough horizontal surface. The object quickly grinds to a halt, due to the net force of friction. If...

First Law: Particles in Two-dimensional Equilibrium

First Law: Particles in Two-dimensional Equilibrium

Recall that a particle in equilibrium is one for which the external forces are balanced. Static equilibrium involves objects at rest, and dynamic equilibrium involves objects in motion without acceleration; but it is important to remember that these conditions are relative. For instance, an object may be at rest when viewed from one frame of reference, but that same object would appear to be in motion when viewed by someone moving at a constant velocity.
Newton's first law tells us about...

Angular Momentum: Single Particle

Angular Momentum: Single Particle

Angular momentum is directed perpendicular to the plane of the rotation, and its magnitude depends on the choice of the origin. The perpendicular vector joining the linear momentum vector of an object to the origin is called the “lever arm.” If the lever arm and linear momentum are collinear, then the magnitude of the angular momentum is zero. Therefore, in this case, the object rotates about the origin such that it lies on the rim of the circumference defined by the lever arm...

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Related Experiment Video

Updated: Feb 17, 2026

Multiscale Sampling of a Heterogeneous Water/Metal Catalyst Interface using Density Functional Theory and Force-Field Molecular Dynamics

Multiscale Sampling of a Heterogeneous Water/Metal Catalyst Interface using Density Functional Theory and Force-Field Molecular Dynamics

Published on: April 12, 2019

Probing many-body dynamics on a 51-atom quantum simulator.

Hannes Bernien¹, Sylvain Schwartz^1,2, Alexander Keesling¹

¹Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA.

|December 1, 2017

Summary

Researchers created controllable quantum matter using cold atoms and Rydberg interactions, realizing a programmable quantum spin model. This system exhibits phase transitions and robust dynamics, paving the way for quantum simulations and algorithms.

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Multiscale Sampling of a Heterogeneous Water/Metal Catalyst Interface using Density Functional Theory and Force-Field Molecular Dynamics

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Area of Science:

Quantum physics
Quantum simulation
Condensed matter physics

Background:

Controllable quantum systems are crucial for understanding quantum matter.
Quantum simulators offer a path to new quantum phases and computational advantages.

Purpose of the Study:

To demonstrate a method for creating controlled many-body quantum matter.
To realize and study a programmable quantum spin model.

Main Methods:

Utilizing deterministically prepared, reconfigurable arrays of individually trapped cold atoms.
Employing excitation to Rydberg states for strong, coherent interactions.
Implementing a programmable Ising-type quantum spin model up to 51 qubits.

Main Results:

Observation of phase transitions into spatially ordered states breaking discrete symmetries.
Verification of high-fidelity preparation of these ordered states.
Investigation of robust many-body dynamics, including persistent oscillations after quantum quenches.

Conclusions:

The developed method enables exploration of many-body phenomena on a programmable quantum simulator.
This approach could facilitate the realization of novel quantum algorithms.
The system provides insights into fundamental properties of quantum matter.