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

54.3K
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.
54.3K
The Pauli Exclusion Principle03:06

The Pauli Exclusion Principle

57.0K
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:
57.0K
Atomic Nuclei: Nuclear Spin State Overview01:03

Atomic Nuclei: Nuclear Spin State Overview

1.4K
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 one, the...
1.4K
Quantum Numbers02:43

Quantum Numbers

46.6K
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.
46.6K
Atomic Nuclei: Nuclear Spin State Population Distribution01:14

Atomic Nuclei: Nuclear Spin State Population Distribution

1.5K
Near absolute zero temperatures, in the presence of a magnetic field, the majority of nuclei prefer the lower energy spin-up state to the higher energy spin-down state. As temperatures increase, the energy from thermal collisions distributes the spins more equally between the two states. The Boltzmann distribution equation gives the ratio of the number of spins predicted in the spin −½ (N−) and spin +½ (N+) states.
1.5K
The Uncertainty Principle04:08

The Uncertainty Principle

29.5K
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...
29.5K

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

Inverted Oscillator Quantum States in the Probability Representation.

Entropy (Basel, Switzerland)·2023

Related Experiment Video

Updated: Nov 6, 2025

A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference
07:56

A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference

Published on: September 5, 2019

8.7K

Probability Representation of Quantum States.

Olga V Man'ko1, Vladimir I Man'ko1,2,3,4

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

Entropy (Basel, Switzerland)
|May 5, 2021
PubMed
Summary

This review introduces a new quantum mechanics formulation using probability distributions. It maps quantum states to these distributions, simplifying quantum evolution equations for various systems.

Keywords:
dequantizerprobability distributionquantizerqubitstar–producttomography

More Related Videos

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

14.8K
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

9.3K

Related Experiment Videos

Last Updated: Nov 6, 2025

A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference
07:56

A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference

Published on: September 5, 2019

8.7K
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

14.8K
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

9.3K

Area of Science:

  • Quantum Mechanics
  • Mathematical Physics
  • Statistical Mechanics

Background:

  • Conventional quantum mechanics uses wave functions and density operators to describe quantum states.
  • Representing quantum states as probability distributions offers a potentially more intuitive approach.
  • Existing methods for probability representations have limitations for certain quantum systems.

Purpose of the Study:

  • To present a novel formulation of quantum mechanics where quantum states are identified with probability distributions.
  • To develop an invertible mapping from standard quantum mechanical descriptions (density operators, wave functions) to probability distributions.
  • To reformulate fundamental quantum equations in a classical-like, probability-based framework.

Main Methods:

  • Construction of an invertible map using Born's rule and dequantizer-quantizer operators.
  • Application of the mapping to systems with continuous and discrete variables.
  • Detailed study of probability representations for qubits, harmonic oscillators, and free particles.

Main Results:

  • An invertible map is established for converting density operators and wave functions to probability distributions.
  • Schrödinger and von Neumann equations are reformulated as linear, classical-like equations for probability distributions.
  • The dynamics of open quantum systems are also expressed in this probability distribution framework.

Conclusions:

  • The new formulation provides a consistent probability distribution representation of quantum mechanics.
  • This approach simplifies the description of quantum states and their evolution, drawing parallels to classical mechanics.
  • The method offers potential for new insights into quantum systems and their relationship with classical physics.