Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

The Quantum-Mechanical Model of an Atom

The Quantum-Mechanical Model of an Atom

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.

The Pauli Exclusion Principle

The Pauli Exclusion Principle

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:

Maxwell-Boltzmann Distribution: Problem Solving

Maxwell-Boltzmann Distribution: Problem Solving

Individual molecules in a gas move in random directions, but a gas containing numerous molecules has a predictable distribution of molecular speeds, which is known as the Maxwell-Boltzmann distribution, f(v).
This distribution function f(v) is defined by saying that the expected number N (v1,v2) of particles with speeds between v1 and v2 is given by

Gauss's Law

Gauss's Law

If a closed surface does not have any charge inside where an electric field line can terminate, then the electric field line entering the surface at one point must necessarily exit at some other point of the surface. Therefore, if a closed surface does not have any charges inside the enclosed volume, then the electric flux through the surface is zero. What happens to the electric flux if there are some charges inside the enclosed volume? Gauss's law gives a quantitative answer to this question.

Symmetry in Maxwell's Equations

Symmetry in Maxwell's Equations

Once the fields have been calculated using Maxwell's four equations, the Lorentz force equation gives the force that the fields exert on a charged particle moving with a certain velocity. The Lorentz force equation combines the force of the electric field and of the magnetic field on the moving charge. Maxwell's equations and the Lorentz force law together encompass all the laws of electricity and magnetism. The symmetry that Maxwell introduced into his mathematical framework may not be...

Quantum Numbers

Quantum Numbers

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.

You might also read

Related Articles

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

Sort by

Same author

Floquet thermalization by power-law induced permutation symmetry breaking.

Physical review. E·2026

Same author

Disordering a permutation symmetric system: Revivals, thermalization, and chaos.

Physical review. E·2025

Same author

Chaos controlled and disorder driven phase transitions induced by breaking permutation symmetry.

Scientific reports·2025

Same author

Primary prevention in Psychiatry in India - An overview of the current state of affairs.

General hospital psychiatry·2025

Same author

The promises and challenges of many-body quantum technologies: A focus on quantum engines.

Nature communications·2024

Same author

Bath Engineering Enhanced Quantum Critical Engines.

Entropy (Basel, Switzerland)·2023

Search research articles

Related Experiment Video

Updated: Aug 28, 2025

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Exactly solvable one-dimensional quantum models with gamma matrices.

Yash Chugh¹, Kusum Dhochak¹, Uma Divakaran¹

¹Department of Physics, Indian Institute of Technology Palakkad, Palakkad 678 623, India.

Physical Review. E

|September 16, 2022

Summary

Researchers developed exactly solvable quantum models using gamma matrices, leading to quadratic Fermionic Hamiltonians. This approach allows exploration of quantum phase transitions in these novel one-dimensional systems.

More Related Videos

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

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

Published on: May 27, 2020

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

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

Published on: August 2, 2019

Related Experiment Videos

Last Updated: Aug 28, 2025

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

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

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

Published on: May 27, 2020

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

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

Published on: August 2, 2019

Area of Science:

Quantum mechanics
Condensed matter physics
High-energy physics

Background:

One-dimensional quantum models like XY and Ising are fundamental in condensed matter physics.
Generalizing these models often leads to complex, non-solvable systems.
Gamma matrices offer a unique mathematical framework for constructing quantum models.

Purpose of the Study:

To introduce exactly solvable generalizations of one-dimensional quantum XY and Ising-like models.
To demonstrate the utility of 2^{d}-dimensional gamma matrices in constructing these models.
To explore quantum phase transitions within the generalized models.

Main Methods:

Utilizing 2^{d}-dimensional gamma matrices as degrees of freedom on each site.
Applying Jordan-Wigner-like transformations to derive quadratic Fermionic Hamiltonians.
Investigating a specific case with four-dimensional gamma matrices.

Main Results:

Successfully constructed exactly solvable generalizations of quantum XY and Ising-like models.
Demonstrated that these models yield quadratic Fermionic Hamiltonians.
Identified and explored quantum phase transitions in the specific four-dimensional gamma matrix case.

Conclusions:

The use of gamma matrices provides an effective method for creating exactly solvable quantum models.
The derived quadratic Fermionic Hamiltonians facilitate the analysis of quantum phase transitions.
This framework offers new avenues for studying complex quantum phenomena in one-dimensional systems.