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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

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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.

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

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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...

The Pauli Exclusion Principle

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The arrangement of electrons in the orbitals of an atom is called its electron configuration. We describe an electron configuration with a symbol that contains three pieces of information:

Periodic Classification of the Elements

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The periodic table arranges atoms based on increasing atomic number so that elements with the same chemical properties recur periodically. When their electron configurations are added to the table, a periodic recurrence of similar electron configurations in the outer shells of these elements is observed. Because they are in the outer shells of an atom, valence electrons play the most important role in chemical reactions. The outer electrons have the highest energy of the electrons in an atom...

Atomic Orbitals

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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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Updated: Jan 21, 2026

Gradient Echo Quantum Memory in Warm Atomic Vapor

Gradient Echo Quantum Memory in Warm Atomic Vapor

Published on: November 11, 2013

Quantum Hypercube States.

L A Howard¹, T J Weinhold¹, F Shahandeh²

¹Centre for Engineered Quantum Systems, School of Mathematics and Physics, University of Queensland, Brisbane, Australia.

Physical Review Letters

|August 7, 2019

Summary

This summary is machine-generated.

We introduce novel quantum hypercube states, exhibiting unique phase-space features for highly sensitive measurements. These states demonstrate robustness against noise, confirmed in a proof-of-principle optomechanics experiment.

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Area of Science:

Quantum optics
Quantum information theory
Continuous-variable quantum systems

Background:

Quantum states with unique phase-space geometries are crucial for advancing quantum technologies.
Understanding Wigner negativity is key to identifying non-classical states.
Optomechanical systems offer a platform for testing fundamental quantum phenomena.

Purpose of the Study:

To introduce and characterize a new class of continuous-variable quantum states: quantum hypercube states.
To investigate the sensitivity and robustness of these states to external perturbations.
To experimentally verify the predicted properties of quantum hypercube states in an optomechanical setup.

Main Methods:

Generating quantum hypercube states via orthographic projection of hypercubes onto phase space.
Theoretical analysis of state sensitivity to displacements and robustness to thermal noise.
Conducting a high-temperature optomechanics experiment to observe state signatures.

Main Results:

Quantum hypercube states exhibit phase-space features smaller than Planck's constant and significant Wigner negativity.
These states show enhanced sensitivity to small-scale displacements, robust against thermal occupation.
Experimental observation of the characteristic outer-edge vertex structure of hypercube states was achieved.

Conclusions:

Quantum hypercube states represent a promising resource for precision measurements due to their unique properties.
The demonstrated robustness opens avenues for practical quantum sensing applications.
The experimental validation confirms the theoretical predictions and the potential of these states.