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Differential Form of Maxwell's Equations01:17

Differential Form of Maxwell's Equations

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James Clerk Maxwell (1831–1879) was one of the significant contributors to physics in the nineteenth century. He is probably best known for having combined existing knowledge of the laws of electricity and the laws of magnetism with his insights to form a complete overarching electromagnetic theory, represented by Maxwell's equations. The four basic laws of electricity and magnetism were discovered experimentally through the work of physicists such as Oersted, Coulomb, Gauss, and...
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Magnetic Fields01:27

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A moving charge or a current creates a magnetic field in the surrounding space, in addition to its electric field. The magnetic field exerts a force on any other moving charge or current that is present in the field. Like an electric field, the magnetic field is also a vector field. At any position, the direction of the magnetic field is defined as the direction in which the north pole of a compass needle points.
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Potential Due to a Magnetized Object01:24

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Magnetic dipoles in magnetic materials are aligned when placed under an external magnetic field. For paramagnets and ferromagnets, dipole alignment occurs in the direction of the magnetic field. However, the dipoles align opposite to the field in the case of diamagnets. This state of magnetic polarization due to the external field is called magnetization. Magnetization is defined as the dipole moment per unit volume. It plays a similar role to polarization in electrostatics.
The vector...
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Electric Field Lines01:25

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The three-dimensional representation of the electric field of a positive point charge requires tracing the electric field vectors, whose lengths decrease as the square of their distance from the charge and which point away from the charge at each point. This vector field is no doubt challenging to visualize. The visualization of electric fields becomes quickly intractable as the number of charges increases.
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The Principle of Superposition and the Gravitational Field01:17

The Principle of Superposition and the Gravitational Field

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The principle of superposition applies to gravitational forces of objects that are sufficiently far apart. It states that the net gravitational force on a point object is the vector sum of the gravitational forces on it due to various objects. The principle helps calculate the force by listing the individual forces and then vectorially summing them up. However, it should be noted that the principle of superposition is not always apparent. In the presence of a second force, the first force could...
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Energy Carried By Electromagnetic Waves01:22

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Anyone who has used a microwave oven knows there is energy in electromagnetic waves. Sometimes, this energy is obvious, such as in the summer sun's warmth. At other times, it is subtle, such as the unfelt energy of gamma rays, which can destroy living cells. Electromagnetic waves bring energy into a system through their electric and magnetic fields. These fields can exert forces and move charges in the system and, thus, do work on them. However, there is energy in an electromagnetic wave,...
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Related Experiment Video

Updated: Nov 26, 2025

Generation and Coherent Control of Pulsed Quantum Frequency Combs
06:42

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

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Mean-field density matrix decompositions.

Janus J Eriksen1

  • 1School of Chemistry, University of Bristol, Cantock's Close, Bristol BS8 1TS, United Kingdom.

The Journal of Chemical Physics
|December 9, 2020
PubMed
Summary
This summary is machine-generated.

We developed new methods to decompose quantum chemistry calculations using localized orbitals. This enhances machine learning models by providing more detailed data for predicting molecular properties.

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Area of Science:

  • Quantum Chemistry
  • Computational Chemistry
  • Materials Science

Background:

  • Mean-field theories like Hartree-Fock and Density Functional Theory are fundamental in quantum chemistry.
  • Accurate prediction of molecular properties relies on robust theoretical frameworks.
  • Understanding electron distribution is key to rationalizing chemical phenomena.

Purpose of the Study:

  • To introduce novel, robust decompositions for mean-field Hartree-Fock and Kohn-Sham density functional theory.
  • To enable partitioning of one-electron reduced density matrices into atomic and bond contributions.
  • To enhance machine learning models in quantum chemistry through improved data granularity.

Main Methods:

  • Utilizing localized molecular orbitals for robust decompositions.
  • Implementing physically sound charge population protocols.
  • Partitioning one-electron reduced density matrices into bond-wise or atomic contributions.
  • Comparing new decompositions against literature alternatives for molecular energies and dipole moments.

Main Results:

  • The new decompositions are lossless, providing accurate partitioning of electronic properties.
  • Demonstrated ability to expose and amplify compositional features for machine learning.
  • Showcased improvements in granularity of data for quantum chemistry machine learning.
  • Preliminary results suggest enhanced structure-property inferences.

Conclusions:

  • Decomposed mean-field theory offers a powerful interpretative tool for electronic phenomena.
  • The developed methods significantly improve data granularity for machine-learned quantum chemistry.
  • Future work can refine structure-property inferences by leveraging increased dataset complexity.