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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.

Molecular Comparison of Gases, Liquids, and Solids

Molecular Comparison of Gases, Liquids, and Solids

Particles in a solid are tightly packed together (fixed shape) and often arranged in a regular pattern; in a liquid, they are close together with no regular arrangement (no fixed shape); in a gas, they are far apart with no regular arrangement (no fixed shape). Particles in a solid vibrate about fixed positions (cannot flow) and do not generally move in relation to one another; in a liquid, they move past each other (can flow) but remain in essentially constant contact; in a gas, they move...

Rise of Liquid in a Capillary Tube

Rise of Liquid in a Capillary Tube

When very thin cylindrical tubes, called capillaries, are dipped in a liquid, the liquid rises or falls in the tube compared to the surrounding liquid. This phenomenon is called capillary action. Capillary action occurs due to the combination of two opposing forces: the cohesive forces of the liquid, which cause it to stick to itself and form a rounded shape, and the adhesive forces between the liquid and the walls of the container, which cause the liquid to be attracted to the container walls.

2D NMR: Heteronuclear Single-Quantum Correlation Spectroscopy (HSQC)

2D NMR: Heteronuclear Single-Quantum Correlation Spectroscopy (HSQC)

Heteronuclear single-quantum correlation spectroscopy (HSQC) is a 2D NMR technique that reveals one-bond correlations between hydrogen and a heteronucleus. The HSQC experiment is similar to the heteronuclear correlation experiment (HETCOR) but is more sensitive. In the HSQC spectrum, the proton chemical shift is plotted on the horizontal F2 axis, while the 13C chemical shift is plotted on the vertical F1 axis. The corresponding proton and 13C spectra are also shown. The HSQC contour plot does...

Deriving the Speed of Sound in a Liquid

Deriving the Speed of Sound in a Liquid

As with waves on a string, the speed of sound or a mechanical wave in a fluid depends on the fluid's elastic modulus and inertia. The two relevant physical quantities are the bulk modulus and the density of the material. Indeed, it turns out that the relationship between speed and the bulk modulus and density in fluids is the same as that between the speed and the Young's modulus and density in solids.
The speed of sound in fluids can be derived by considering a mechanical wave...

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Updated: Jan 25, 2026

Fabrication and Testing of Microfluidic Optomechanical Oscillators

Fabrication and Testing of Microfluidic Optomechanical Oscillators

Published on: May 29, 2014

Quantum Optomechanics in a Liquid.

A B Shkarin¹, A D Kashkanova¹, C D Brown¹

¹Department of Physics, Yale University, New Haven, Connecticut 06520, USA.

Physical Review Letters

|May 4, 2019

Summary

This summary is machine-generated.

Researchers measured quantum fluctuations in superfluid helium using an optical cavity. This study reveals superfluid helium

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Area of Science:

Quantum optics
Condensed matter physics
Cavity optomechanics

Background:

Quantum fluctuations are fundamental to quantum mechanics.
Superfluid helium exhibits unique quantum properties.
Cavity optomechanics studies the interaction between light and mechanical motion.

Purpose of the Study:

To measure quantum fluctuations of an acoustic mode in superfluid helium.
To investigate the interplay between superfluid helium and optical cavities.
To explore new frontiers in quantum optomechanics.

Main Methods:

Coupling a single acoustic mode in superfluid helium to an optical cavity.
Monitoring scattered light (Stokes and anti-Stokes) from an acoustic wave.
Analyzing signal intensity and cross-correlation.

Main Results:

Observed characteristic features of acoustic zero-point motion.
Detected quantum backaction from intracavity light.
Demonstrated quantum optomechanical effects in superfluid helium.

Conclusions:

Quantum fluctuations in superfluid helium can be measured using optical cavities.
Superfluid helium offers a novel platform for quantum optomechanics.
This work paves the way for exploring new quantum phenomena in superfluids.