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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.

Alkyl Halides

Alkyl Halides

Structural Properties
Alkyl halides are halogen-substituted alkanes wherein one or more hydrogen atoms of an alkane is replaced by a halogen atom such as fluorine, chlorine, bromine, or iodine. The carbon atom in an alkyl halide is bonded to the halogen atom, which is sp3-hybridized and exhibits a tetrahedral shape.
Unlike alkyl halides, compounds in which a halogen atom is bonded to an sp2 -hybridized carbon atom of a carbon-carbon double bond (C=C) are called vinyl halides. Whereas aryl...

Dot Product

Dot Product

The dot product is an essential concept in mathematics and physics.
In engineering, the dot product of any two vectors is the product of the magnitudes of the vectors and the cosine of the angle between them. It is denoted by a dot symbol between the two vectors.
Consider a vehicle pulling an object along the ground using a rope. If the rope makes an angle with the horizontal axis, the work done can be calculated using the dot product of the force applied and the object's displacement.
The dot...

The Dot Product

The Dot Product

Measuring how one directional quantity affects another along a specific path involves comparing their orientation and strength. When two such quantities are represented using direction and amount, a numerical result is computed to show how much one acts along the path of the other. This result comes from a rule combining both inputs' horizontal and vertical parts and adding the results.This calculation gives a single value that grows larger when both inputs point in similar directions and...

Acid Halides to Esters: Alcoholysis

Acid Halides to Esters: Alcoholysis

Alcoholysis is a nucleophilic acyl substitution reaction in which an alcohol functions as a nucleophile. Acid halides react with alcohol to produce esters. The mechanism proceeds in three steps:

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Related Experiment Video

Updated: Feb 2, 2026

Facile Synthesis of Colloidal Lead Halide Perovskite Nanoplatelets via Ligand-Assisted Reprecipitation

Facile Synthesis of Colloidal Lead Halide Perovskite Nanoplatelets via Ligand-Assisted Reprecipitation

Published on: October 1, 2019

Superfluorescence from lead halide perovskite quantum dot superlattices.

Gabriele Rainò^1,2,3, Michael A Becker^4,5, Maryna I Bodnarchuk⁶

¹Department of Chemistry and Applied Bioscience, Institute of Inorganic Chemistry, ETH Zurich, Zurich, Switzerland. rainog@ethz.ch.

|November 9, 2018

Summary

Superfluorescence, a quantum light phenomenon, was achieved in perovskite nanocrystals. Highly ordered nanocrystal superlattices enable intense, coherent light bursts, overcoming previous limitations.

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Low Pressure Vapor-assisted Solution Process for Tunable Band Gap Pinhole-free Methylammonium Lead Halide Perovskite Films

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Published on: September 8, 2017

Area of Science:

Quantum Optics
Materials Science
Nanotechnology

Background:

Superfluorescence is a quantum phenomenon involving collective light emission from an ensemble of excited emitters.
Achieving superfluorescence requires precise control over emitter interactions and environmental decoupling, limiting its observation to specific systems.
Colloidal nanocrystals, despite their potential as photonic sources, have not exhibited superfluorescence due to emission broadening and fast dephasing.

Purpose of the Study:

To demonstrate superfluorescence in colloidal perovskite nanocrystals.
To investigate the potential of self-organized perovskite nanocrystal superlattices for generating coherent light phenomena.

Main Methods:

Fabrication of highly ordered three-dimensional superlattices using caesium lead halide (CsPbX3) perovskite nanocrystals.
Characterization of optical properties, including emission dynamics, coherence times, and photon statistics, under high excitation density.

Main Results:

Observed key signatures of superfluorescence in perovskite nanocrystal superlattices, including dynamically red-shifted emission and accelerated radiative decay (>20-fold).
Demonstrated extended first-order coherence time (>4-fold), photon bunching, and Burnham-Chiao ringing behavior.
Achieved mesoscopically extended coherent states in a novel nanocrystal system.

Conclusions:

Self-organized perovskite nanocrystal superlattices can exhibit superfluorescence, overcoming previous material limitations.
These findings open possibilities for enhanced optoelectronic devices and novel quantum light sources.
The study highlights the potential of engineered nanocrystal assemblies for advanced quantum optical applications.