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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.

NMR Spectroscopy: Spin–Spin Coupling

NMR Spectroscopy: Spin–Spin Coupling

The spin state of an NMR-active nucleus can have a slight effect on its immediate electronic environment. This effect propagates through the intervening bonds and affects the electronic environments of NMR-active nuclei up to three bonds away; occasionally, even farther. This phenomenon is called spin–spin coupling or J-coupling. Coupling interactions are mutual and result in small changes in the absorption frequencies of both nuclei involved. While nuclei of the same element are involved...

Spin–Spin Coupling: One-Bond Coupling

Spin–Spin Coupling: One-Bond Coupling

Coupling interactions are strongest between NMR-active nuclei bonded to each other, where spin information can be transmitted directly through the pair of bonding electrons. While nuclei polarize their electrons to the opposite spins, the bonding electron pair has opposite spins. Configurations with antiparallel nuclear spins are expected to be lower in energy. When coupling makes antiparallel states more favorable, J is considered to have a positive value. The one-bond coupling constant, 1J,...

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...

Spin–Spin Coupling: Two-Bond Coupling (Geminal Coupling)

Spin–Spin Coupling: Two-Bond Coupling (Geminal Coupling)

Two NMR-active nuclei bonded to a central atom can be involved in geminal or two-bond coupling. Geminal coupling is commonly seen between diastereotopic protons in chiral molecules and unsymmetrical alkenes, among others.
The central atom need not be NMR-active because its electrons are affected by the electron polarization of the spin-active atoms. However, spin information is transmitted less effectively than in one-bond coupling, and 2J values are usually weaker than 1J values. The energy of...

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Related Experiment Video

Updated: Feb 12, 2026

Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform

Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform

Published on: August 2, 2019

Probing the strongly driven spin-boson model in a superconducting quantum circuit.

L Magazzù¹, P Forn-Díaz^2,3,4,5, R Belyansky^2,6

¹Institute of Physics, University of Augsburg, Universitätsstraße 1, D-86135, Augsburg, Germany.

Nature Communications

|April 13, 2018

Summary

Intense driving of quantum systems amplifies environmental effects, suppressing coherence. Tuning drive amplitude can induce a transition from coherent to incoherent states in dissipative quantum systems.

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Area of Science:

Quantum physics
Open quantum systems
Quantum information science

Background:

Quantum two-level systems interacting with their environment lose quantum coherence, a phenomenon described by the spin-boson model.
Understanding the impact of external driving on these dissipative systems is crucial for quantum technologies.

Purpose of the Study:

To investigate how intense coherent driving affects a strongly dissipative quantum system, specifically a superconducting qubit.
To explore the realization of the driven Ohmic spin-boson model in a superconducting circuit.

Main Methods:

Experimental investigation of a superconducting qubit coupled to an electromagnetic environment under coherent drive.
Theoretical analysis of the driven Ohmic spin-boson model.

Main Results:

Coherent driving was shown to reinforce the environmental suppression of quantum coherence.
A transition from a coherent to an incoherent state was achieved by adjusting the drive amplitude.
An out-of-equilibrium detailed balance relation was experimentally demonstrated.

Conclusions:

The study advances the fundamental understanding of driven open quantum systems.
Results offer potential pathways for designing entangled light-matter states.