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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.

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.

Limiting Reactant

Limiting Reactant

The relative amounts of reactants and products represented in a balanced chemical equation are often referred to as stoichiometric amounts. However, in reality, the reactants are not always present in the stoichiometric amounts indicated by the balanced equation.

Metallic Solids

Metallic Solids

Metallic solids such as crystals of copper, aluminum, and iron are formed by metal atoms. The structure of metallic crystals is often described as a uniform distribution of atomic nuclei within a “sea” of delocalized electrons. The atoms within such a metallic solid are held together by a unique force known as metallic bonding that gives rise to many useful and varied bulk properties.
All metallic solids exhibit high thermal and electrical conductivity, metallic luster, and malleability....

Structures of Solids

Structures of Solids

Solids in which the atoms, ions, or molecules are arranged in a definite repeating pattern are known as crystalline solids. Metals and ionic compounds typically form ordered, crystalline solids. A crystalline solid has a precise melting temperature because each atom or molecule of the same type is held in place with the same forces or energy. Amorphous solids or non-crystalline solids (or, sometimes, glasses) which lack an ordered internal structure and are randomly arranged. Substances that...

Spin–Spin Coupling Constant: Overview

Spin–Spin Coupling Constant: Overview

In bromoethane, the three methyl protons are coupled to the two methylene protons that are three bonds away. In accordance with the n+1 rule, the signal from the methyl protons is split into three peaks with 1:2:1 relative intensities. The methylene protons appear as a quartet, with the relative intensities of 1:3:3:1.
Qualitatively, any spin plus-half nucleus polarizes the spins of its electrons to the minus-half state. Consequently, the paired electron in the hydrogen–carbon bond must...

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Related Experiment Video

Updated: Jan 22, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Overcoming Frequency Resolution Limits Using a Solid-State Spin Quantum Sensor.

Qingyun Cao¹, Genko T Genov¹, Yaoming Chu²

¹Ulm University, Institute for Quantum Optics, Albert-Einstein-Allee 11, Ulm 89081, Germany.

Physical Review Letters

|January 20, 2026

Summary

This summary is machine-generated.

Superresolution quantum sensing overcomes fundamental spectroscopy limits by resolving closely spaced incoherent signals. This quantum approach enhances frequency resolution beyond classical capabilities.

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Last Updated: Jan 22, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs

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Published on: January 10, 2019

Area of Science:

Quantum physics
Spectroscopy
Metrology

Background:

Spectroscopy relies on precise frequency separation.
Distinguishing close, incoherent signals is limited by resolution.
Quantum projection noise hinders signal distinguishability.

Purpose of the Study:

To demonstrate a superresolution quantum sensing approach.
To overcome classical frequency resolution limitations.
To resolve nearly identical incoherent signals.

Main Methods:

Utilizing a solid-state spin quantum sensor.
Applying superresolution conditions with specific interrogation times.
Reducing classical readout noise with nuclear spin assistance.

Main Results:

Experimental resolution of two nearly identical incoherent signals.
Elimination of quantum projection noise.
Achieved sub-kHz resolution with 80 μs signal detection time.
Resolution scaling as t^{-2}, surpassing the standard t^{-1}.

Conclusions:

Quantum sensing offers a path beyond conventional frequency resolution limits.
The demonstrated method significantly improves precision measurements.
Highlights the potential of quantum technologies in metrology.