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

42.7K
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.
42.7K
Atomic Nuclei: Nuclear Spin State Overview01:03

Atomic Nuclei: Nuclear Spin State Overview

1.1K
NMR-active nuclei have energy levels called 'spin states' that are associated with the orientations of their nuclear magnetic moments. In the absence of a magnetic field, the nuclear magnetic moments are randomly oriented, and the spin states are degenerate. When an external magnetic field is applied, the spin states have only 2 + 1 orientations available to them. A proton with = ½ has two available orientations. Similarly, for a quadrupolar nucleus with a nuclear spin value of...
1.1K
The Pauli Exclusion Principle03:06

The Pauli Exclusion Principle

42.6K
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:
42.6K
The Bohr Model02:18

The Bohr Model

59.1K
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...
59.1K
Quantum Numbers02:43

Quantum Numbers

35.0K
It is said that the energy of an electron in an atom is quantized; that is, it can be equal only to certain specific values and can jump from one energy level to another but not transition smoothly or stay between these levels.
35.0K
Molecular Orbital Theory I02:35

Molecular Orbital Theory I

32.4K
Overview of Molecular Orbital Theory
32.4K

You might also read

Related Articles

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

Sort by
Same author

Even and Odd Cat States of Two and Three Qubits in the Probability Representation of Quantum Mechanics.

Entropy (Basel, Switzerland)·2024
Same author

Not All Probability Density Functions Are Tomograms.

Entropy (Basel, Switzerland)·2024
Same author

Bosonic Representation of Matrices and Angular Momentum Probabilistic Representation of Cyclic States.

Entropy (Basel, Switzerland)·2023
Same author

Probability Distributions Describing Qubit-State Superpositions.

Entropy (Basel, Switzerland)·2023
Same author

Dynamics of System States in the Probability Representation of Quantum Mechanics.

Entropy (Basel, Switzerland)·2023
Same author

Quantum Oscillator at Temperature <i>T</i> and the Evolution of a Charged-Particle State in the Electric Field in the Probability Representation of Quantum Mechanics.

Entropy (Basel, Switzerland)·2023

Related Experiment Video

Updated: Aug 9, 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

14.6K

Inverted Oscillator Quantum States in the Probability Representation.

Olga V Man'ko1, Vladimir I Man'ko1,2

  • 1Lebedev Physical Institute, Russian Academy of Sciences, Leninskii Prospect 53, Moscow 119991, Russia.

Entropy (Basel, Switzerland)
|February 25, 2023
PubMed
Summary

This study introduces a probability representation for quantum states using the quantizer-dequantizer formalism. It compares quantum and classical probability distributions, presenting examples for parametric and inverted oscillators.

Keywords:
dequantizer operatorprobability distributionsquantizer operator

More Related Videos

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

9.1K
Gradient Echo Quantum Memory in Warm Atomic Vapor
10:00

Gradient Echo Quantum Memory in Warm Atomic Vapor

Published on: November 11, 2013

12.9K

Related Experiment Videos

Last Updated: Aug 9, 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

14.6K
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

9.1K
Gradient Echo Quantum Memory in Warm Atomic Vapor
10:00

Gradient Echo Quantum Memory in Warm Atomic Vapor

Published on: November 11, 2013

12.9K

Area of Science:

  • Quantum mechanics
  • Statistical mechanics

Background:

  • The probability representation offers a unique perspective on quantum states.
  • Understanding quantum probability distributions is crucial for characterizing quantum systems.

Purpose of the Study:

  • To develop a probability representation for quantum system states using the quantizer-dequantizer formalism.
  • To compare this quantum representation with classical probability representations.
  • To illustrate the formalism with examples of specific quantum systems.

Main Methods:

  • Application of the quantizer-dequantizer formalism.
  • Construction of probability distributions for quantum states.
  • Comparative analysis of quantum and classical probability representations.

Main Results:

  • A novel probability representation for quantum states was successfully constructed.
  • Key differences and similarities between quantum and classical probability representations were identified.
  • Probability distributions for parametric and inverted oscillators were derived and presented.

Conclusions:

  • The quantizer-dequantizer formalism provides a viable method for constructing quantum probability representations.
  • The developed formalism facilitates a deeper understanding of quantum systems by bridging classical and quantum probability concepts.
  • The presented examples demonstrate the applicability of the method to diverse quantum systems.