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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)

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...

Phase Transitions

Phase Transitions

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Classical Conditioning

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Associative learning, a core principle in behavioral psychology, involves forming connections between events and facilitating learned responses. This concept is vividly illustrated by classical conditioning, a process extensively studied by the Russian physiologist Ivan Pavlov. Pavlov's pioneering research on dogs' digestive systems led to the discovery that behaviors can be learned through association, laying the groundwork for classical conditioning.
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Properties of Transition Metals

Properties of Transition Metals

Transition metals are defined as those elements that have partially filled d orbitals. As shown in Figure 1, the d-block elements in groups 3–12 are transition elements. The f-block elements, also called inner transition metals (the lanthanides and actinides), also meet this criterion because the d orbital is partially occupied before the f orbitals.

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Related Experiment Video

Updated: Feb 13, 2026

Gradient Echo Quantum Memory in Warm Atomic Vapor

Gradient Echo Quantum Memory in Warm Atomic Vapor

Published on: November 11, 2013

Quantum Speed Limits across the Quantum-to-Classical Transition.

B Shanahan¹, A Chenu², N Margolus²

¹Department of Physics, University of Massachusetts, Boston, Massachusetts 02125, USA.

Physical Review Letters

|March 16, 2018

Summary

This summary is machine-generated.

Quantum and classical systems both have speed limits, contrary to popular belief. These fundamental limits on evolution rates are determined by the generator of time evolution in both quantum and classical physics.

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Last Updated: Feb 13, 2026

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Area of Science:

Quantum physics
Classical mechanics
Theoretical physics

Background:

Quantum speed limits define the maximum rate of change for quantum systems.
Understanding these limits across the quantum-to-classical transition is crucial for foundational physics.

Purpose of the Study:

To explore quantum speed limits using a phase-space approach.
To identify and characterize equivalent speed limits in classical systems.
To investigate the existence of speed limits in classical mechanics.

Main Methods:

Utilized a phase-space approach to analyze quantum evolution.
Derived and compared speed limit formulations for quantum and classical dynamics.
Investigated the mathematical structure of the generator of time evolution.

Main Results:

Demonstrated that speed limits exist for both quantum and classical systems.
Showed that classical speed limits are analogous to quantum ones, determined by the norm of the generator of time evolution.
Challenged the common assumption that speed limits are exclusive to quantum mechanics.

Conclusions:

Speed limits are a universal feature of physical systems, applying to both quantum and classical regimes.
The generator of time evolution plays a fundamental role in defining these limits across different physical frameworks.
This work provides new insights into the quantum-to-classical transition and the nature of physical law.