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 Uncertainty Principle04:08

The Uncertainty Principle

27.0K
Werner Heisenberg considered the limits of how accurately one can measure properties of an electron or other microscopic particles. He determined that there is a fundamental limit to how accurately one can measure both a particle’s position and its momentum simultaneously. The more accurate the measurement of the momentum of a particle is known, the less accurate the position at that time is known and vice versa. This is what is now called the Heisenberg uncertainty principle. He...
27.0K
The Quantum-Mechanical Model of an Atom02:45

The Quantum-Mechanical Model of an Atom

51.1K
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.
51.1K
The Pauli Exclusion Principle03:06

The Pauli Exclusion Principle

53.0K
The arrangement of electrons in the orbitals of an atom is called its electron configuration. We describe an electron configuration with a symbol that contains three pieces of information:
53.0K
Parseval's Theorem01:18

Parseval's Theorem

708
Parseval's theorem is a fundamental concept in signal processing and harmonic analysis. It asserts that for a periodic function, the average power of the signal over one period equals the sum of the squared magnitudes of all its complex Fourier coefficients. This theorem, named after Marc-Antoine Parseval, provides a powerful tool for analyzing the energy distribution in signals.
Interestingly, Parseval's theorem also holds for the trigonometric form of the Fourier series, which...
708
The de Broglie Wavelength02:32

The de Broglie Wavelength

29.0K
In the macroscopic world, objects that are large enough to be seen by the naked eye follow the rules of classical physics. A billiard ball moving on a table will behave like a particle; it will continue traveling in a straight line unless it collides with another ball, or it is acted on by some other force, such as friction. The ball has a well-defined position and velocity or well-defined momentum, p = mv, which is defined by mass m and velocity v at any given moment. This is the typical...
29.0K
The Bohr Model02:18

The Bohr Model

71.6K
Following the work of Ernest Rutherford and his colleagues in the early twentieth century, the picture of atoms consisting of tiny dense nuclei surrounded by lighter and even tinier electrons continually moving about the nucleus was well established. This picture was called the planetary model since it pictured the atom as a miniature “solar system” with the electrons orbiting the nucleus like planets orbiting the sun. The simplest atom is hydrogen, consisting of a single proton as...
71.6K

You might also read

Related Articles

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

Sort by
Same author

Properties of the simplest localized molecular orbitals: The P-LMOs.

The Journal of chemical physics·2025
Same author

Knowles Partitioning from a Stationary Condition: Single- and Multireference Case.

Journal of chemical theory and computation·2025
Same author

Combining Strongly Orthogonal Geminals with Explicitly Correlated Corrections.

Journal of chemical theory and computation·2025
Same author

Knowles Partitioning at the Multireference Level.

The journal of physical chemistry. A·2024
Same author

Analysis and Assessment of Knowles' Partitioning in Many-Body Perturbation Theory.

Journal of chemical theory and computation·2024
Same author

Pivot invariance of multiconfiguration perturbation theory via frame vectors.

The Journal of chemical physics·2022
Same journal

Characteristic polynomials, spectral-based Riemann-Zeta functions and entropy indices of n-dimensional hypercubes.

Journal of mathematical chemistry·2023
Same journal

Rényi's divergence as a chemical similarity criterion.

Journal of mathematical chemistry·2021
Same journal

Biochemical and phylogenetic networks-II: <i>X</i>-trees and phylogenetic trees.

Journal of mathematical chemistry·2021
Same journal

Biochemical and phylogenetic networks-I: hypertrees and corona products.

Journal of mathematical chemistry·2021
Same journal

Descriptors of 2D-dynamic graphs as a classification tool of DNA sequences.

Journal of mathematical chemistry·2020
Same journal

Graphical and numerical representations of DNA sequences: statistical aspects of similarity.

Journal of mathematical chemistry·2020
See all related articles

Related Experiment Video

Updated: Oct 2, 2025

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators
09:23

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators

Published on: May 30, 2014

14.7K

The function in quantum theory II. Mathematical challenges and paradoxa.

Zs É Mihálka1,2, M Nooijen3, Á Margócsy1,2

  • 1Institute of Chemistry, Laboratory of Theoretical Chemistry, ELTE Loránd Eötvös University, P.O.B. 32, Budapest 112, 1518 Hungary.

Journal of Mathematical Chemistry
|February 28, 2022
PubMed
Summary
This summary is machine-generated.

Researchers postulate a generalized function, the square root of Dirac

Keywords:
Gamma functionKinetic postulateSquare root of Dirac-delta

More Related Videos

Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform
05:39

Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform

Published on: August 2, 2019

9.8K
Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit
05:30

Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit

Published on: September 8, 2023

676

Related Experiment Videos

Last Updated: Oct 2, 2025

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators
09:23

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators

Published on: May 30, 2014

14.7K
Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform
05:39

Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform

Published on: August 2, 2019

9.8K
Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit
05:30

Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit

Published on: September 8, 2023

676

Area of Science:

  • Theoretical Physics
  • Quantum Mechanics
  • Mathematical Physics

Background:

  • The square root of Dirac's delta function is not formally defined in standard mathematical frameworks.
  • Existing quantum mechanical treatments provide accurate energies for systems like the H atom and 1D harmonic oscillator.

Purpose of the Study:

  • To explore the implications of a postulated generalized function, the square root of Dirac's delta function.
  • To investigate its potential for quasi-classical treatments of quantum systems.
  • To identify and collect paradoxical situations arising from its use.

Main Methods:

  • Postulating the existence of the square root of Dirac's delta function.
  • Applying this generalized function to simple quantum systems (H atom, 1D harmonic oscillator).
  • Analyzing the resulting mathematical and physical implications.

Main Results:

  • A generalized function, termed the square root of Dirac's delta function, has been defined.
  • This function allows for a quasi-classical treatment of specific quantum systems.
  • The application of this function leads to paradoxical situations.

Conclusions:

  • The defined square root of Dirac's delta function is a novel mathematical entity, distinct from traditional functions or distributions.
  • Rigorous mathematical frameworks for its consistent treatment are yet to be established.
  • Further scientific community input is required to resolve the identified paradoxa.