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The Quantum-Mechanical Model of an Atom02:45

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.
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Quantum Numbers02:43

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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.
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Proteins perform many mechanical functions in a cell. These proteins can be classified into two general categories- proteins that generate mechanical forces and proteins that are subjected to mechanical forces. Proteins providing mechanical support to the structure of the cell, such as keratin, are subjected to mechanical force, whereas proteins involved in cell movement and transport of molecules across cell membranes, such as an ion pump, are examples of generating mechanical force. 
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Antibody Structure01:10

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Overview
Antibodies, also known as immunoglobulins (Ig), are essential players of the adaptive immune system. These antigen-binding proteins are produced by B cells and make up 20 percent of the total blood plasma by weight. In mammals, antibodies fall into five different classes, which each elicits a different biological response upon antigen binding.
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Viruses are extraordinarily diverse in shape and size, but they all have several structural features in common. All viruses have a core that contains a DNA- or RNA-based genome. The core is surrounded by a protective coat of proteins called the capsid. The capsid is composed of subunits called capsomeres. The capsid and genome-containing core are together known as the nucleocapsid.
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Reaction Mechanisms03:06

Reaction Mechanisms

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Chemical reactions often occur in a stepwise fashion, involving two or more distinct reactions taking place in a sequence. A balanced equation indicates the reacting species and the product species, but it reveals no details about how the reaction occurs at the molecular level. The reaction mechanism (or reaction path) provides details regarding the precise, step-by-step process by which a reaction occurs.
For instance, the decomposition of ozone appears to follow a mechanism with two steps:
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Related Experiment Video

Updated: Feb 3, 2026

Versatile Technique to Produce a Hierarchical Design in Nanoporous Gold
05:28

Versatile Technique to Produce a Hierarchical Design in Nanoporous Gold

Published on: February 10, 2023

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Completely top-down hierarchical structure in quantum mechanics.

Yakir Aharonov1,2,3, Eliahu Cohen4,5, Jeff Tollaksen6,2

  • 1Institute for Quantum Studies, Chapman University, Orange, CA 92866; yakir@post.tau.ac.il eli17c@gmail.com.

Proceedings of the National Academy of Sciences of the United States of America
|October 24, 2018
PubMed
Summary
This summary is machine-generated.

Complex quantum systems cannot be fully understood by examining their smallest parts. Higher-order quantum correlations can dictate lower-order ones, but not the reverse, suggesting a top-down structure.

Keywords:
emergencequantum mechanicsreductionismtop–downweak values

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Area of Science:

  • Quantum mechanics
  • Many-body systems
  • Foundations of physics

Background:

  • Investigates the limits of inductive reasoning in characterizing complex systems.
  • Explores whether system behavior can be reduced to its fundamental components.
  • Addresses the relationship between subsystem properties and overall system behavior.

Purpose of the Study:

  • To determine if large quantum systems can be fully characterized by their subsystems.
  • To investigate the reducibility of complex system behavior to atomic-level interactions.
  • To analyze the nature of correlations in quantum mechanics.

Main Methods:

  • Introduces a two-particle example demonstrating strong correlations.
  • Applies concepts to atomic and electromagnetic systems.
  • Develops a general construction using pre- and postselected ensembles.

Main Results:

  • Demonstrates that higher-order quantum correlations can determine lower-order ones.
  • Shows that lower-order correlations provide no information about higher-order correlations.
  • Highlights that N-body correlations can be global properties under 'strictly local' measurements.

Conclusions:

  • Answers the question of reducibility in the negative for specific systems and measurements.
  • Supports a top-down structure in many-body quantum mechanics.
  • Suggests that global properties can emerge from local constraints in quantum systems.