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

The Quantum-Mechanical Model of an Atom02:45

The Quantum-Mechanical Model of an Atom

42.9K
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.
42.9K
UV–Vis Spectroscopy: Molecular Electronic Transitions01:16

UV–Vis Spectroscopy: Molecular Electronic Transitions

1.7K
In Ultraviolet–Visible (UV–Vis) spectroscopy, the absorption of electromagnetic radiation is used to probe the electronic structure of molecules. This technique provides insights into molecular electronic transitions, particularly the movement of electrons between different molecular orbitals. Radiation is absorbed if the energy of the electromagnetic radiation passing through the molecule is precisely equal to the energy difference between the excited and ground states. During this...
1.7K
The Energies of Atomic Orbitals03:21

The Energies of Atomic Orbitals

24.3K
In an atom, the negatively charged electrons are attracted to the positively charged nucleus. In a multielectron atom, electron-electron repulsions are also observed. The attractive and repulsive forces are dependent on the distance between the particles, as well as the sign and magnitude of the charges on the individual particles. When the charges on the particles are opposite, they attract each other. If both particles have the same charge, they repel each other.
24.3K
Electric Field of a Non Uniformly Charged Sphere01:22

Electric Field of a Non Uniformly Charged Sphere

1.6K
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...
1.6K
Electrostatic Boundary Conditions in Dielectrics01:27

Electrostatic Boundary Conditions in Dielectrics

1.4K
When an electric field passes from one homogeneous medium to another, crossing the boundary between the two mediums imparts a discontinuity in the electric field. This results in electrostatic boundary conditions that depend on the type of mediums the field propagates through.
Consider a case where both the mediums across a boundary are two different dielectric materials. Recall that the electric field and electric displacement are proportional and related through the material's...
1.4K
Electrostatic Boundary Conditions01:16

Electrostatic Boundary Conditions

571
Consider an external electric field propagating through a homogeneous medium. When the electric field crosses the surface boundary of the medium, it undergoes a discontinuity. The electric field can be resolved into normal and tangential components. The amount by which the field changes at any boundary is given by the difference between the field components above and below the surface boundary.
The surface integral of an electric field is given by Gauss's law in integral form and is related to...
571

You might also read

Related Articles

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

Sort by
Same author

Approximation of magnetic Schrödinger operators with <math><mi>δ</mi></math> -interactions supported on networks.

Letters in mathematical physics·2026
Same author

Nonrelativistic Limit of Generalized MIT Bag Models and Spectral Inequalities.

Mathematical physics, analysis, and geometry·2024
Same author

Schrödinger Operators with Oblique Transmission Conditions in <math></math>.

Communications in mathematical physics·2023
Same author

Dirac operator spectrum in tubes and layers with a zigzag-type boundary.

Letters in mathematical physics·2022
Same author

A unified approach to Schrödinger evolution of superoscillations and supershifts.

Journal of evolution equations·2022
Same author

Self-Adjoint Dirac Operators on Domains in <math> </math>.

Annales Henri Poincare·2020
Same journal

Quadratic Subproduct Systems, Free Products, and Their C*-Algebras.

Integral equations and operator theory·2026
Same journal

Models of Holomorphic Functions on the Symmetrized Skew Bidisc.

Integral equations and operator theory·2026
Same journal

Function theory on the annulus in the dp-norm.

Integral equations and operator theory·2025
Same journal

The Double-Layer Potential for Spectral Constants Revisited.

Integral equations and operator theory·2025
Same journal

Coupled Domain-Boundary Variational Formulations for Hodge-Helmholtz Operators.

Integral equations and operator theory·2022
See all related articles

Related Experiment Video

Updated: Aug 29, 2025

ARL Spectral Fitting as an Application to Augment Spectral Data via Franck-Condon Lineshape Analysis and Color Analysis
07:11

ARL Spectral Fitting as an Application to Augment Spectral Data via Franck-Condon Lineshape Analysis and Color Analysis

Published on: August 19, 2021

2.6K

Spectral Transition for Dirac Operators with Electrostatic -Shell Potentials Supported on the Straight Line.

Jussi Behrndt1, Markus Holzmann1, Matěj Tušek2

  • 1Institut für Angewandte Mathematik, Technische Universität Graz, Steyrergasse 30, 8010 Graz, Austria.

Integral Equations and Operator Theory
|September 5, 2022
PubMed
Summary
This summary is machine-generated.

We studied the 2D Dirac operator with an electrostatic shell interaction. At critical strengths, the continuous spectrum collapses to a single point within the spectral gap.

Keywords:
Boundary tripleDirac operatorSingular potentialSpectral transition

More Related Videos

Vibrational Spectra of a N719-Chromophore/Titania Interface from Empirical-Potential Molecular-Dynamics Simulation, Solvated by a Room Temperature Ionic Liquid
08:54

Vibrational Spectra of a N719-Chromophore/Titania Interface from Empirical-Potential Molecular-Dynamics Simulation, Solvated by a Room Temperature Ionic Liquid

Published on: January 25, 2020

5.7K
Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids
08:04

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids

Published on: May 27, 2020

8.5K

Related Experiment Videos

Last Updated: Aug 29, 2025

ARL Spectral Fitting as an Application to Augment Spectral Data via Franck-Condon Lineshape Analysis and Color Analysis
07:11

ARL Spectral Fitting as an Application to Augment Spectral Data via Franck-Condon Lineshape Analysis and Color Analysis

Published on: August 19, 2021

2.6K
Vibrational Spectra of a N719-Chromophore/Titania Interface from Empirical-Potential Molecular-Dynamics Simulation, Solvated by a Room Temperature Ionic Liquid
08:54

Vibrational Spectra of a N719-Chromophore/Titania Interface from Empirical-Potential Molecular-Dynamics Simulation, Solvated by a Room Temperature Ionic Liquid

Published on: January 25, 2020

5.7K
Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids
08:04

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids

Published on: May 27, 2020

8.5K

Area of Science:

  • Quantum mechanics
  • Mathematical physics
  • Relativistic quantum mechanics

Background:

  • The Dirac operator is fundamental in relativistic quantum mechanics.
  • Investigating spectral properties of operators with interactions is crucial.
  • Shell interactions introduce unique mathematical challenges.

Purpose of the Study:

  • To analyze the spectral properties of the 2D Dirac operator with a specific electrostatic shell interaction.
  • To identify and characterize spectral transitions under varying interaction strengths.
  • To understand the behavior of the continuous spectrum near critical interaction strengths.

Main Methods:

  • The study employs mathematical analysis of the 2D Dirac operator.
  • Focus is on the spectral properties, particularly the continuous spectrum.
  • The behavior is examined at critical strengths of the electrostatic shell interaction.

Main Results:

  • A spectral transition is observed in the Dirac operator.
  • For critical interaction strengths, the continuous spectrum collapses.
  • This collapse occurs to a single point within the spectral gap of the free Dirac operator.

Conclusions:

  • The electrostatic shell interaction significantly alters the Dirac operator's spectrum.
  • Critical interaction strengths lead to a dramatic spectral collapse.
  • This finding provides insight into the behavior of relativistic quantum systems with localized interactions.