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

Equivalent Couples01:28

Equivalent Couples

In mechanical engineering, the concept of equivalent couples plays a crucial role in understanding and analyzing various mechanical systems.
Two couples are considered to be equivalent if they produce the same rotational effect on a rigid body. In other words, the two couples have the same magnitude and act in the same direction, causing the same angular displacement or acceleration in the body.
For instance, consider two couples lying in the plane of the page, with one having a pair of equal...
First Law: Particles in Two-dimensional Equilibrium01:18

First Law: Particles in Two-dimensional Equilibrium

Recall that a particle in equilibrium is one for which the external forces are balanced. Static equilibrium involves objects at rest, and dynamic equilibrium involves objects in motion without acceleration; but it is important to remember that these conditions are relative. For instance, an object may be at rest when viewed from one frame of reference, but that same object would appear to be in motion when viewed by someone moving at a constant velocity.
Newton's first law tells us about the...
The Pauli Exclusion Principle03:06

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:
Reduced Mass Coordinates: Isolated Two-body Problem01:12

Reduced Mass Coordinates: Isolated Two-body Problem

In classical mechanics, the two-body problem is one of the fundamental problems describing the motion of two interacting bodies under gravity or any other central force. When considering the motion of two bodies, one of the most important concepts is the reduced mass coordinates, a quantity that allows the two-body problem to be solved like a single-body problem. In these circumstances, it is assumed that a single body with reduced mass revolves around another body fixed in a position with an...
Symmetry in Maxwell's Equations01:28

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...
First Law: Particles in One-dimensional Equilibrium01:10

First Law: Particles in One-dimensional Equilibrium

Newton's first law of motion states that a body at rest remains at rest, or if in motion, remains in motion at constant velocity, unless acted on by a net external force. It also states that there must be a cause for any change in velocity (a change in either magnitude or direction) to occur. This cause is a net external force. For example, consider what happens to an object sliding along a rough horizontal surface. The object quickly grinds to a halt, due to the net force of friction. If we...

You might also read

Related Articles

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

Sort by
Same author

AutoSTOP-RT-TDDFT: Adaptive and Selected Real-Time Time-Dependent Density Functional Theory for Simulation of X-Ray Absorptions.

Journal of computational chemistry·2026
Same author

Fully self-gated dual-venc five-dimensional flow magnetic resonance imaging for simultaneous imaging of the cardiovascular and portal venous systems: A feasibility study.

Journal of cardiovascular magnetic resonance : official journal of the Society for Cardiovascular Magnetic Resonance·2026
Same author

GraphLooper: predicting chromatin loops based on hierarchical multi-view graph pooling method.

Briefings in bioinformatics·2026
Same author

Hydrogen evolution electrocatalysts in high-fold degenerate topological semimetals with chiral structures.

Communications chemistry·2026
Same author

CodeSafetyBench evaluating and improving ethical safety in large language model code generation.

iScience·2026
Same author

Unified MPI Parallelization of Wave Function Methods: iCIPT2 as a Showcase.

Journal of chemical theory and computation·2026
Same journal

Quantum simulation of alignment dependent differential cross sections in co-propagating molecular beams at cold collision energies.

The Journal of chemical physics·2026
Same journal

Non-additive ion effects on the coil-globule equilibrium of a generic polymer in aqueous salt solutions.

The Journal of chemical physics·2026
Same journal

Insights into the unexpected small reduction of the temperature of maximum density of water by lithium chloride addition.

The Journal of chemical physics·2026
Same journal

Optical frequency comb double-resonance spectroscopy of the 9030-9175 cm-1 states of ethylene.

The Journal of chemical physics·2026
Same journal

Time reversal breaking of colloidal particles in cells.

The Journal of chemical physics·2026
Same journal

Photodynamics of amino acids under UV excitation: Extraterrestrial amino acids.

The Journal of chemical physics·2026
See all related articles

Related Experiment Video

Updated: Jun 21, 2026

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

Exact two-component Hamiltonians revisited.

Wenjian Liu1, Daoling Peng

  • 1Beijing National Laboratory for Molecular Sciences, Institute of Theoretical and Computational Chemistry, College of Chemistry and Molecular Engineering, Peking University, Beijing 100871, People's Republic of China. liuwj@pku.edu.cn

The Journal of Chemical Physics
|July 24, 2009
PubMed
Summary
This summary is machine-generated.

Two methods for deriving two-component Hamiltonians were compared. A previously unknown error in the standard Dirac-to-Schrodinger picture transformation was identified, leading to corrected, equivalent formulations.

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

Related Experiment Videos

Last Updated: Jun 21, 2026

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

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

Area of Science:

  • Quantum Chemistry
  • Relativistic Quantum Mechanics

Background:

  • Deriving accurate two-component Hamiltonians is crucial for relativistic quantum chemistry.
  • Existing methods often involve approximations or complex transformations.

Purpose of the Study:

  • To compare two distinct routes for deriving exact two-component Hamiltonians.
  • To identify and correct potential errors in established theoretical frameworks.

Main Methods:

  • Direct block diagonalization of the Dirac operator in a kinetically balanced basis.
  • Utilizing the Foldy-Wouthuysen operator with resolutions of the identity.

Main Results:

  • The two derivation routes initially yielded surprisingly different Hamiltonian expressions.
  • A subtle error in the standard Dirac to Schrodinger picture transformation was uncovered in the first method.
  • Correction of this error rendered both formulations equivalent.

Conclusions:

  • The standard method for deriving two-component Hamiltonians contains a subtle error.
  • A corrected, unified approach to deriving exact two-component Hamiltonians is now established.
  • This work clarifies theoretical inconsistencies in relativistic quantum mechanical calculations.