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

Second Uniqueness Theorem01:16

Second Uniqueness Theorem

2.7K
Consider a region consisting of several individual conductors with a definite charge density in the region between these conductors. The second uniqueness theorem states that if the total charge on each conductor and the charge density in the in-between region are known, then the electric field can be uniquely determined.
In contrast, consider that the electric field is non-unique and apply Gauss's law in divergence form in the region between the conductors and the integral form to the surface...
2.7K
Electromagnetic Fields01:30

Electromagnetic Fields

3.0K
Electric fields generated by static charges, often referred to as electrostatic fields, are characteristically different from electric fields created by time-varying magnetic fields. While the former is a conservative field, implying that no net work is done on a test charge if it goes around in a complete loop in the field, the latter is, by definition, not a conservative field; net work is done, and it is proportional to the rate of change of magnetic flux.
However, the observation of...
3.0K
Electric Field of a Non Uniformly Charged Sphere01:22

Electric Field of a Non Uniformly Charged Sphere

2.5K
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...
2.5K
Magnetostatic Boundary Conditions01:28

Magnetostatic Boundary Conditions

1.8K
An electric field suffers a discontinuity at a surface charge. Similarly, a magnetic field is discontinuous at a surface current. The perpendicular component of a magnetic field is continuous across the interface of two magnetic mediums. In contrast, its parallel component, perpendicular to the current, is discontinuous by the amount equal to the product of the vacuum permeability and the surface current. Like the scalar potential in electrostatics, the vector potential is also continuous...
1.8K
Maxwell's Equation Of Electromagnetism01:29

Maxwell's Equation Of Electromagnetism

4.4K
James Clerk Maxwell (1831–1879) was one of the major contributors to physics in the nineteenth century. Although he died young, he made major contributions to the development of the kinetic theory of gases, to the understanding of color vision, and to understanding the nature of Saturn's rings. He is probably best known for having combined existing knowledge on the laws of electricity and magnetism with his insights into a complete overarching electromagnetic theory, which is...
4.4K
Differential Form of Maxwell's Equations01:17

Differential Form of Maxwell's Equations

1.4K
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...
1.4K

You might also read

Related Articles

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

Sort by
Same author

Perspectives on determinism in quantum mechanics: Born, Bohm, and the "Quantal Newtonian" laws.

The Journal of chemical physics·2022
Same author

A non-perturbative study of the interplay between electron-phonon interaction and Coulomb interaction in undoped graphene.

Journal of physics. Condensed matter : an Institute of Physics journal·2022
Same author

The 'Quantal Newtonian' First Law: A Complementary Perspective to the Stationary-state Quantum Theory of Electrons.

Chemphyschem : a European journal of chemical physics and physical chemistry·2022
Same author

Wigner high-electron-correlation regime of nonuniform density systems: A quantal-density-functional-theory study.

Physical review. A, Atomic, molecular, and optical physics·2019
Same author

Wigner High Electron Correlation Regime in Nonuniform Electron Density Systems: Kinetic and Correlation-Kinetic Aspects.

Computational & theoretical chemistry·2019
Same author

Generalization of the Schrödinger Theory of Electrons.

Journal of computational chemistry·2017

Related Experiment Video

Updated: Mar 30, 2026

Finite Element Modelling of a Cellular Electric Microenvironment
08:23

Finite Element Modelling of a Cellular Electric Microenvironment

Published on: May 18, 2021

4.1K

Hohenberg-Kohn theorems in electrostatic and uniform magnetostatic fields.

Xiao-Yin Pan1, Viraht Sahni2

  • 1Department of Physics, Ningbo University, Ningbo 315211, China.

The Journal of Chemical Physics
|November 9, 2015
PubMed
Summary

The Hohenberg-Kohn theorems are generalized to include electrostatic and magnetostatic fields. This work proves bijective relationships between potentials and ground-state densities for electrons with and without spin.

More Related Videos

Optimized Setup and Protocol for Magnetic Domain Imaging with In Situ Hysteresis Measurement
09:43

Optimized Setup and Protocol for Magnetic Domain Imaging with In Situ Hysteresis Measurement

Published on: November 7, 2017

10.0K
Electric and Magnetic Field Devices for Stimulation of Biological Tissues
13:29

Electric and Magnetic Field Devices for Stimulation of Biological Tissues

Published on: May 15, 2021

5.9K

Related Experiment Videos

Last Updated: Mar 30, 2026

Finite Element Modelling of a Cellular Electric Microenvironment
08:23

Finite Element Modelling of a Cellular Electric Microenvironment

Published on: May 18, 2021

4.1K
Optimized Setup and Protocol for Magnetic Domain Imaging with In Situ Hysteresis Measurement
09:43

Optimized Setup and Protocol for Magnetic Domain Imaging with In Situ Hysteresis Measurement

Published on: November 7, 2017

10.0K
Electric and Magnetic Field Devices for Stimulation of Biological Tissues
13:29

Electric and Magnetic Field Devices for Stimulation of Biological Tissues

Published on: May 15, 2021

5.9K

Area of Science:

  • Quantum Chemistry
  • Condensed Matter Physics
  • Theoretical Physics

Background:

  • The Hohenberg-Kohn (HK) theorems establish a fundamental link between external potentials and ground-state properties in quantum mechanics.
  • These theorems are crucial for density functional theory (DFT), enabling calculations based on electron density rather than wavefunctions.

Purpose of the Study:

  • To generalize the Hohenberg-Kohn theorems to include external electrostatic and magnetostatic fields.
  • To establish variational principles for electron density and current density under these generalized conditions.
  • To extend the validity of these theorems to include spin and degenerate states.

Main Methods:

  • Mathematical proofs rigorously establishing the bijectivity between external potentials (scalar and vector) and ground-state densities (including current density).
  • Introduction of new constraints, such as fixed canonical orbital angular momentum and spin angular momentum, for generalized theorems.
  • Application of the Percus-Levy-Lieb constrained-search approach to extend validity to N-representable and degenerate states.

Main Results:

  • Proof of generalized HK theorems for arbitrary electrostatic fields and fixed electron number.
  • Demonstration of bijective relationships between potentials and ground-state densities/current densities in the presence of uniform magnetostatic fields.
  • Extension of these theorems to include electron spin and degenerate states with fixed angular momenta.

Conclusions:

  • The study provides a rigorous mathematical foundation for density functional theory in the presence of external electromagnetic fields.
  • The generalized theorems offer a broader applicability of DFT for systems with complex potentials and spin interactions.
  • This work paves the way for more accurate theoretical investigations of electronic structures in magnetic materials and under external fields.