Dirac Hamiltonian
E505997
Hamiltonian operator
generator of time evolution
observable
quantum mechanical operator
relativistic Hamiltonian
self-adjoint operator
unbounded operator
The Dirac Hamiltonian is the relativistic quantum-mechanical energy operator for spin-½ particles, incorporating both special relativity and spin via the Dirac equation.
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
Hamiltonian operator
ⓘ
generator of time evolution ⓘ observable ⓘ quantum mechanical operator ⓘ relativistic Hamiltonian ⓘ self-adjoint operator ⓘ unbounded operator ⓘ |
| actsOn |
Dirac spinor
ⓘ
four-component spinor wavefunction ⓘ |
| associatedWith | Dirac sea concept ⓘ |
| basedOn | Dirac equation NERFINISHED ⓘ |
| commutesWith | total angular momentum operator ⓘ |
| couplesTo | electromagnetic four-potential ⓘ |
| describes |
relativistic fermions
ⓘ
spin-1/2 particles ⓘ |
| doesNotCommuteWith | orbital angular momentum operator ⓘ |
| eigenvaluesInclude |
negative energy spectrum
ⓘ
positive energy spectrum ⓘ |
| formulatedIn |
quantum field theory
ⓘ
relativistic quantum mechanics ⓘ |
| generatorOf | time evolution of Dirac spinors ⓘ |
| hasSymmetry |
Lorentz covariance (in covariant form)
ⓘ
parity (for free particle) ⓘ time translation invariance (for time-independent case) ⓘ |
| hasTerm |
interaction term
ⓘ
kinetic term ⓘ mass term ⓘ |
| implements | minimal coupling prescription ⓘ |
| incorporates |
special relativity
ⓘ
spin degrees of freedom ⓘ |
| introducedBy | Paul Dirac NERFINISHED ⓘ |
| introducedIn | 1928 ⓘ |
| predicts |
electron spin
ⓘ
existence of antiparticles ⓘ magnetic moment of the electron ⓘ |
| reducesTo |
Pauli Hamiltonian in the nonrelativistic limit
ⓘ
Schrödinger Hamiltonian in appropriate limit ⓘ |
| relatedTo | Klein-Gordon operator NERFINISHED ⓘ |
| satisfies | relativistic energy-momentum relation ⓘ |
| usedFor |
description of electrons in external electromagnetic fields
ⓘ
fine structure calculations ⓘ relativistic hydrogen atom ⓘ relativistic scattering problems ⓘ |
| usedIn |
quantum electrodynamics
ⓘ
relativistic atomic physics ⓘ |
| usesMatrix |
Dirac alpha matrices
ⓘ
Dirac beta matrix NERFINISHED ⓘ gamma matrices ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.