Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Gravitation Between Spherically Symmetric Masses01:14

Gravitation Between Spherically Symmetric Masses

1.1K
The gravitational potential energy between two spherically symmetric bodies can be calculated from the masses and the distance between the bodies, assuming that the center of mass is concentrated at the respective centers of the bodies.
1.1K
Gauss's Law: Spherical Symmetry01:26

Gauss's Law: Spherical Symmetry

8.6K
A charge distribution has spherical symmetry if the density of charge depends only on the distance from a point in space and not on the direction. In other words, if the system is rotated, it doesn't look different. For instance, if a sphere of radius R is uniformly charged with charge density ρ0, then the distribution has spherical symmetry. On the other hand, if a sphere of radius R is charged so that the top half of the sphere has a uniform charge density ρ1 and the bottom half has a...
8.6K
Gauss's Law: Cylindrical Symmetry01:20

Gauss's Law: Cylindrical Symmetry

8.8K
A charge distribution has cylindrical symmetry if the charge density depends only upon the distance from the axis of the cylinder and does not vary along the axis or with the direction about the axis. In other words, if a system varies if it is rotated around the axis or shifted along the axis, it does not have cylindrical symmetry. In real systems, we do not have infinite cylinders; however, if the cylindrical object is considerably longer than the radius from it that we are interested in,...
8.8K
Spherical Coordinates01:23

Spherical Coordinates

13.2K
Spherical coordinate systems are preferred over Cartesian, polar, or cylindrical coordinates for systems with spherical symmetry. For example, to describe the surface of a sphere, Cartesian coordinates require all three coordinates. On the other hand, the spherical coordinate system requires only one parameter: the sphere's radius. As a result, the complicated mathematical calculations become simple. Spherical coordinates are used in science and engineering applications like electric and...
13.2K
The Principle of Superposition and the Gravitational Field01:17

The Principle of Superposition and the Gravitational Field

1.8K
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...
1.8K
Electric Field of a Non Uniformly Charged Sphere01:22

Electric Field of a Non Uniformly Charged Sphere

2.0K
Gauss's law states that the electric flux through any closed surface equals the net charge enclosed within the surface. This law is beneficial for determining the expressions for the electric field for a particular charge distribution if the electric flux is known.
Consider a non-uniformly charged sphere, for which the density of charge depends only on the distance from a point in space and not on the direction. Such a sphere has a spherically symmetrical charge distribution. Here, the electric...
2.0K

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Spherical potential functional theory.

The Journal of chemical physics·2021
Same author

Information theoretical and thermodynamic view of the excited-state density functional theory of Coulomb systems.

The Journal of chemical physics·2020
Same author

A thermal orbital-free density functional approach.

The Journal of chemical physics·2019
Same author

Density functional theory from spherically symmetric densities.

The Journal of chemical physics·2018

Related Experiment Video

Updated: Nov 16, 2025

Studying Large Amplitude Oscillatory Shear Response of Soft Materials
06:07

Studying Large Amplitude Oscillatory Shear Response of Soft Materials

Published on: April 25, 2019

13.2K

Subspace theory with spherically symmetric densities.

Á Nagy1

  • 1Department of Theoretical Physics, University of Debrecen, H-4002 Debrecen, Hungary.

The Journal of Chemical Physics
|February 20, 2021
PubMed
Summary

A novel theory extends unique density-potential mapping to degenerate atomic states. This work derives key equations and presents a new virial theorem for these complex systems.

Area of Science:

  • Quantum Chemistry
  • Atomic Physics
  • Density Functional Theory

Background:

  • Unique determination of Coulomb external potential from non-degenerate electron densities.
  • Need to extend this theory to degenerate states in atoms.

Purpose of the Study:

  • Extend the unique density-potential mapping theory to degenerate electronic states.
  • Derive Euler and Kohn-Sham equations for these states.
  • Present a novel virial theorem applicable to degenerate systems.

Main Methods:

  • Theoretical extension of existing density-potential uniqueness theory.
  • Derivation of Euler and Kohn-Sham equations.
  • Formulation of a new virial theorem.

Main Results:

More Related Videos

Spatial Separation of Molecular Conformers and Clusters
10:37

Spatial Separation of Molecular Conformers and Clusters

Published on: January 9, 2014

11.2K
Longitudinal Morphological and Physiological Monitoring of Three-dimensional Tumor Spheroids Using Optical Coherence Tomography
08:50

Longitudinal Morphological and Physiological Monitoring of Three-dimensional Tumor Spheroids Using Optical Coherence Tomography

Published on: February 9, 2019

8.0K

Related Experiment Videos

Last Updated: Nov 16, 2025

Studying Large Amplitude Oscillatory Shear Response of Soft Materials
06:07

Studying Large Amplitude Oscillatory Shear Response of Soft Materials

Published on: April 25, 2019

13.2K
Spatial Separation of Molecular Conformers and Clusters
10:37

Spatial Separation of Molecular Conformers and Clusters

Published on: January 9, 2014

11.2K
Longitudinal Morphological and Physiological Monitoring of Three-dimensional Tumor Spheroids Using Optical Coherence Tomography
08:50

Longitudinal Morphological and Physiological Monitoring of Three-dimensional Tumor Spheroids Using Optical Coherence Tomography

Published on: February 9, 2019

8.0K
  • Demonstrated unique determination of the Coulomb external potential for degenerate states.
  • Successfully derived Euler and Kohn-Sham equations for degenerate systems.
  • Presented a novel form of the virial theorem.

Conclusions:

  • Degenerate atomic states can be rigorously treated as spherically symmetric using subspace densities.
  • The theory provides a robust framework for understanding degenerate electronic structures.
  • Advances in density functional theory for complex atomic systems.