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Relativistic quantum mechanical wave equation
In particle physics, the Dirac equation is a relativistic wave equation derived by British physicist Paul Dirac in 1928. In its free form, or including
Dirac_equation
British physicist (1902–1984)
on quantum mechanics. Dirac formulated the Dirac equation, one of the most important results in physics, in 1928. The equation connected special relativity
Paul_Dirac
Description of a quantum-mechanical system
turn introducing Dirac matrices. In a modern context, the Klein–Gordon equation describes spin-less particles, while the Dirac equation describes spin-1/2
Schrödinger_equation
Geometric analogue of the Dirac equation
physics, the Dirac–Kähler equation, also known as the Ivanenko–Landau–Kähler equation, is the geometric analogue of the Dirac equation that can be defined
Dirac–Kähler_equation
Generators of the Clifford algebra for relativistic quantum mechanics
to the Dirac equation for relativistic spin 1 2 {\displaystyle {\tfrac {\ 1\ }{2}}} particles. Gamma matrices were introduced by Paul Dirac in 1928
Gamma_matrices
Recoil force on accelerating charged particle
relativistic version is called the Lorentz–Dirac force or collectively known as Abraham–Lorentz–Dirac force. The equations are in the domain of classical physics
Abraham–Lorentz_force
Theoretical model of the vacuum
physicist Paul Dirac in 1930 to explain the anomalous negative-energy quantum states predicted by the relativistically correct Dirac equation for electrons
Dirac_sea
Generalization of the Dirac equation
In mathematical physics, the Dirac equation in curved spacetime is a generalization of the Dirac equation from flat spacetime (Minkowski space) to curved
Dirac equation in curved spacetime
Dirac_equation_in_curved_spacetime
Quantum mechanical equation of motion of charged particles in magnetic field
external electromagnetic field. It is the non-relativistic limit of the Dirac equation and can be used where particles are moving at speeds much less than
Pauli_equation
Relativistic wave equation describing massless fermions
The equation is named after Hermann Weyl. The Weyl fermions are one of the three possible types of elementary fermions, the other two being the Dirac and
Weyl_equation
Linearized quantum-mechanical equation
Lévy-Leblond equation was obtained under similar heuristic derivations as the Dirac equation, but contrary to the latter, the Lévy-Leblond equation is not relativistic
Lévy-Leblond_equation
Condensed matter system
Dirac matter refers to a class of condensed matter systems which can be effectively described by the Dirac equation. Even though the Dirac equation itself
Dirac_matter
Relativistic wave description of fermions
these freedoms. The Majorana equation can be written in several distinct forms: As the Dirac equation written so that the Dirac operator is purely Hermitian
Majorana_equation
identity for the stationary nonlinear Dirac equation in three spatial dimensions (and also the Maxwell-Dirac equations) and in arbitrary spatial dimension
Pokhozhaev's_identity
Generalized function whose value is zero everywhere except at zero
one can approximate the force of the impact by a Dirac delta. In doing so, one can simplify the equations and calculate the motion of the ball by only considering
Dirac_delta_function
Quantum phenomena
1929. Originally, Klein obtained a paradoxical result by applying the Dirac equation to the familiar problem of electron scattering from a potential barrier
Klein_paradox
Field equation for spin-3/2 fermions
Rarita–Schwinger equation is the relativistic field equation for spin-3/2 fermions. It is the spin-3/2 analogue of the Dirac equation for spin-1/2 fermions
Rarita–Schwinger_equation
Quantum mechanics taking into account particles near or at the speed of light
charged particles in electromagnetic fields. The key result is the Dirac equation, from which these predictions emerge automatically. By contrast, in
Relativistic quantum mechanics
Relativistic_quantum_mechanics
Mathematical description of fermions
occur in the relativistic spin-1/2 wave function solutions to the Dirac equation. They are constructed out of two simpler component spinors, the Weyl
Dirac_spinor
Dirac equation for self-interacting fermions
notation. In quantum field theory, the nonlinear Dirac equation is a model of self-interacting Dirac fermions. This model is widely considered in quantum
Nonlinear_Dirac_equation
Quantum effect in some non-metals
of Dirac cone comes from the Dirac equation that can describe relativistic particles in quantum mechanics, proposed by Paul Dirac. Isotropic Dirac cones
Dirac_cone
Atoms with a single valence electron, so they behave like hydrogen
called hydrogen-like ions. The non-relativistic Schrödinger equation and relativistic Dirac equation for the hydrogen atom and hydrogen-like atoms can be solved
Hydrogen-like_atom
Wave equations respecting special and general relativity
of equation (2) to the electron – by various manipulations he factorized the equation into the form and one of these factors is the Dirac equation (see
Relativistic_wave_equations
Quantum number parameterizing spin and angular momentum
and Immanuel Estermann. In 1928, Paul Dirac developed a relativistic wave equation, now termed the Dirac equation, which predicted the spin magnetic moment
Spin_quantum_number
Setting of relativistic physics in geometric algebra
formulation for all of relativistic physics, including the Dirac equation, Maxwell equation and general relativity" and "reduces the mathematical divide
Spacetime_algebra
Mathematical physics equation tied to the Dirac current
the Dirac equation and so it applies only to "on-shell" solutions of the Dirac equation. For any solution ψ {\displaystyle \psi } of the massive Dirac equation
Gordon_decomposition
Action of a massive abelian gauge field
Quantum gravity Vector boson Relativistic wave equations Klein–Gordon equation (spin 0) Dirac equation (spin 1/2) B.R. Martin; G. Shaw (2008), Particle
Proca_action
Clifford algebra in 4 dimensions
was introduced by the mathematical physicist P. A. M. Dirac in 1928 in developing the Dirac equation for spin-1/2 particles with a matrix representation
Dirac_algebra
Type of fermion
pseudo-relativistic Dirac equation. Dirac spinor, a wavefunction-like description of a Dirac fermion Dirac–Kähler fermion, a geometric formulation of Dirac fermions
Dirac_fermion
Complex four-component spinor
plane-wave solutions to the Dirac equation, are standard basis solutions to the Dirac equation describing the propagation of Dirac spinors. These are spinors
Plane-wave solutions to the Dirac equation
Plane-wave_solutions_to_the_Dirac_equation
Wave equation for arbitrary spin particles
named after Valentine Bargmann and Eugene Wigner. Paul Dirac first published the Dirac equation in 1928, and later (1936) extended it to particles of any
Bargmann–Wigner_equations
Atom of the element hydrogen
incorporated in the relativistic Dirac equation, with predictions that come still closer to experiment. Again the Dirac equation may be solved analytically
Hydrogen_atom
Field equation from quantum gravity
Wheeler–DeWitt equation for theoretical physics and applied mathematics, is a field equation attributed to John Archibald Wheeler and Bryce DeWitt. The equation attempts
Wheeler–DeWitt_equation
Relativistic wave equation derived by Gregory Breit in 1929
Breit equation, or Dirac–Coulomb–Breit equation, is a relativistic wave equation derived by Gregory Breit in 1929 based on the Dirac equation, which
Breit_equation
Periodic table of the elements with eight or more periods
it was noted that a simplistic interpretation of the relativistic Dirac equation runs into problems with electron orbitals at Z > 1/α ≈ 137.036 (the
Extended_periodic_table
Equation for two-body bound states
significantly more massive than the other, the system is simplified into the Dirac equation for the light particle under the external potential of the heavy one
Bethe–Salpeter_equation
Algebra of 4D spacetime
{J}}\rangle _{0\oplus 3}\,,} which is a real scalar invariant. The Dirac equation, for an electrically charged particle of mass m and charge e, takes
Algebra_of_physical_space
Relativistic wave equation in quantum mechanics
Paul Dirac and Pascual Jordan. As a result, the equation did not play an important role in the development of quantum mechanics. While the equation virtually
Klein–Gordon_equation
Spin of an electron
from the Dirac equation, a fundamental equation connecting the electron's spin with its electromagnetic properties. Reduction of the Dirac equation for an
Electron_magnetic_moment
First-order differential linear operator on spinor bundle, whose square is the Laplacian
by Paul Dirac. The question which concerned Dirac was to factorise formally the Laplace operator of the Minkowski space, to get an equation for the wave
Dirac_operator
Fields giving rise to fermionic particles
spin-1/2 fermion field is the Dirac field (named after Paul Dirac), and denoted by ψ ( x ) {\displaystyle \psi (x)} . The equation of motion for a free spin
Fermionic_field
Hydrodynamic formulation of the Schrödinger equations
having the Dirac equation written with hydrodynamic variables. In the relativistic case, the Hamilton–Jacobi equation is also the guidance equation, which
Madelung_equations
Functional equation Functional equation (L-function) Constitutive equation Laws of science Defining equation (physical chemistry) List of equations in classical
List_of_equations
Particle effect
Schrödinger in 1930 in his analysis of wave packet solutions of the Dirac equation for relativistic electrons in free space. These exhibit interference
Zitterbewegung
Quantum field theory equations
two-body Dirac equations (TBDE) of constraint dynamics provide a three-dimensional yet manifestly covariant reformulation of the Bethe–Salpeter equation for
Two-body_Dirac_equations
Dynamic disturbance in a medium or field
probability density of a particle. The Dirac equation is a relativistic wave equation detailing electromagnetic interactions. Dirac waves accounted for the fine
Wave
Hypothetical particle with one magnetic pole
charge qm of the source. Dirac was originally considering an electron whose wave function is described by the Dirac equation. Because the electron returns
Magnetic_monopole
Ab initio quantum chemistry program
effects in molecules, using the Dirac equation as its starting point. The program is available in source code form, see DIRAC Homepage for download information
Dirac_(software)
Anti-particle to the electron
Paul Dirac published a paper proposing that electrons can have both a positive and negative charge. This paper introduced the Dirac equation, a unification
Positron
Symmetry of physical laws under a charge-conjugation transformation
solutions of several notable differential equations, including the Klein–Gordon equation and the Dirac equation, a symmetry of the corresponding quantum
C-symmetry
Quantum variations of random walks
)\otimes |0\rangle } Consider what happens when we discretize a massive Dirac operator over one spatial dimension. In the absence of a mass term, we have
Quantum_walk
Theoretical framework in physics
infinities in calculations. In 1928, Dirac wrote down a wave equation that described relativistic electrons: the Dirac equation. It had the following important
Quantum_field_theory
Details in the emission spectrum of an atom
can also be obtained from the non-relativistic limit of the Dirac equation, since Dirac's theory naturally incorporates relativity and spin interactions
Fine_structure
Mathematical description of quantum state
satisfy the same equation as do the fields (wave functions) in many cases. Thus the Klein–Gordon equation (spin 0) and the Dirac equation (spin 1⁄2) in this
Wave_function
Function in quantum field theory showing probability amplitudes of moving particles
four dimensions, and employing the Feynman slash notation. This is the Dirac equation for a delta function source in spacetime. Using the momentum representation
Propagator
Intrinsic quantum property of particles
Dirac equation, rather than being a more nearly physical quantity, like orbital angular momentum L). Nevertheless, spin appears in the Dirac equation
Spin_(physics)
Physical field theory with no forces/interactions
Klein-Gordon equation. It is given by ∂ μ ∂ μ ϕ + m 2 ϕ = 0 {\displaystyle \partial ^{\mu }\partial _{\mu }\phi +m^{2}\phi =0} The Dirac equation describes
Free_field
Dual to the Dirac spinor
In quantum field theory, the Dirac adjoint defines the dual operation of a Dirac spinor. The Dirac adjoint is motivated by the need to form well-behaved
Dirac_adjoint
fermion Dirac field Dirac gauge Dirac hole theory Dirac Lagrangian Dirac matrices Dirac matter Dirac membrane Dirac picture Dirac sea Dirac spectrum Dirac spinor
List of things named after Paul Dirac
List_of_things_named_after_Paul_Dirac
Quantum field theory of electromagnetism
the solutions of the Dirac equation, which describe the behavior of the electron's probability amplitude and the Maxwell's equations, which describes the
Quantum_electrodynamics
Bound state of an electron and positron
Positronium can also be considered by a particular form of the two-body Dirac equation; two particles with a Coulomb interaction can be exactly separated in
Positronium
Quantum mechanical phenomenon
Moreover, if quantum tunnelling is modelled with the relativistic Dirac equation, well established mathematical theorems imply that the process is completely
Quantum_tunnelling
Concept in physics
explain the anomaly of negative-energy quantum states predicted by the Dirac equation. A year later, after work by Weyl, the negative energy concept was abandoned
Negative_energy
Relativistic equation relating total energy to mass and momentum
basis for constructing relativistic wave equations, ultimately leading to the development of the Dirac equation, which incorporates the concepts of antimatter
Energy–momentum_relation
Relativistic interaction in quantum physics
the same result would use relativistic quantum mechanics, using the Dirac equation, and would include many-body interactions. Achieving an even more precise
Spin–orbit_interaction
Interpretation of solutions to Dirac's equation
the continuum of negative energy states, that are solutions to the Dirac equation, are filled with electrons, and the vacancies in this continuum (holes)
Dirac_hole_theory
Classical theory of gravitation
address the issue of quantum gravity. In the Einstein–Cartan theory, the Dirac equation becomes nonlinear when it is expressed in terms of the Levi-Civita connection
Einstein–Cartan_theory
Scientific subjects
mechanics was combined with the theory of relativity in the formulation of Paul Dirac. Other developments include quantum statistics, quantum electrodynamics
Branches_of_physics
Effect in quantum electrodynamics
difference was not predicted by theory and it cannot be derived from the Dirac equation, which predicts identical energies. Hence the Lamb shift is a deviation
Lamb_shift
Used to understand the Dirac equation
Wouthuysen in 1949 to understand the nonrelativistic limit of the Dirac equation, the equation for spin-1/2 particles. A detailed general discussion of the
Foldy–Wouthuysen transformation
Foldy–Wouthuysen_transformation
Fermion path integral approach in 1+1 dimensions
spatial dimension. It provides a representation of solutions of the Dirac equation in (1+1)-dimensional spacetime as discrete sums. The model can be visualised
Feynman_checkerboard
Lowest possible energy of a quantum system or field
symbol notation) of the hydrogen atom which was not predicted by the Dirac equation, according to which these states should have the same energy. Charged
Zero-point_energy
Subatomic particle
predicted by Paul Dirac in his 1933 Nobel Prize lecture. Dirac received the Nobel Prize for his 1928 publication of his Dirac equation that predicted the
Antiproton
systems of Dirac operators, the Paneitz operator, Dirac operators on hyperbolic space, the hyperbolic Laplacian and Weinstein equations. In Euclidean
Clifford_analysis
Formula for spectral line wavelengths in alkali metals
dependence, while relativistic and spin corrections appear when the Dirac equation, fine-structure interactions, and quantum electrodynamics (QED) effects
Rydberg_formula
Theory of forces and subatomic particles
of dark matter and neutrino oscillations. In 1928, Paul Dirac introduced the Dirac equation, which implied the existence of antimatter. In 1954, Yang
Standard_Model
Description of physical properties at the atomic and subatomic scale
replacement of the Schrödinger equation with a covariant equation such as the Klein–Gordon equation or the Dirac equation. While these theories were successful
Quantum_mechanics
Physical theory with fields invariant under the action of local "gauge" Lie groups
electron field. The bare-bones action that generates the electron field's Dirac equation is S = ∫ ψ ¯ ( i ℏ c γ μ ∂ μ − m c 2 ) ψ d 4 x {\displaystyle {\mathcal
Gauge_theory
Connection on a spinor bundle
The spin connection arises in the Dirac equation when expressed in the language of curved spacetime, see Dirac equation in curved spacetime. Specifically
Spin_connection
Hexagonal lattice made of carbon atoms
understanding the electronic properties of 3D graphite. The emergent massless Dirac equation was separately pointed out in 1984 by Gordon Walter Semenoff, and by
Graphene
Formulation of the quantum many-body problem
was inappositely thought that the Dirac equation described a relativistic wavefunction (hence the obsolete "Dirac sea" interpretation), rather than a
Second_quantization
explained by reformulating and reinterpreting the Dirac equation as a true field equation. The quantized "Dirac field" or "electron field" was introduced, with
History of quantum field theory
History_of_quantum_field_theory
Function describing an electron in an atom
energy. This approximation is broken slightly in the solution to the Dirac equation (where energy depends on n and another quantum number j), and by the
Atomic_orbital
Connection between correlation functions and the S-matrix
are put on-shell. Recall that solutions to the quantized free-field Dirac equation may be written as Ψ ( x ) = ∑ s = ± ∫ d p ~ ( b p s u p s e i p ⋅ x
LSZ_reduction_formula
Evolutionary equation under renormalization group flow
In physics, the Callan–Symanzik equation is a differential equation describing the evolution of the n-point correlation functions under variation of the
Callan–Symanzik_equation
Non-mathematical introduction
discovered matter wave nature of electrons. In 1928 Paul Dirac published his relativistic wave equation simultaneously incorporating relativity, predicting
Introduction to quantum mechanics
Introduction_to_quantum_mechanics
Partial differential equation
mechanics and information theory, the Fokker–Planck equation is a partial differential equation that describes the time evolution of the probability
Fokker–Planck_equation
Force acting on charged particles in electric and magnetic fields
classical theory. A complete relativistic treatment is given by the Dirac equation, which incorporates spin and electromagnetic interactions through minimal
Lorentz_force
Physical constant in quantum mechanics
fresh apple. Many equations in quantum physics are customarily written using the reduced Planck constant, also known as the Dirac constant, equal to
Planck_constant
Interpretation of quantum mechanics
are the Dirac matrices, and e μ i {\displaystyle e_{\mu }^{i}} is a tetrad. If the wave function propagates according to the curved Dirac equation, then
De_Broglie–Bohm_theory
entanglement spinor, spinor group, spinor bundle Dirac sea Spin foam Poincaré group gamma matrices Dirac adjoint Wigner's classification anyon Copenhagen
List of mathematical topics in quantum theory
List_of_mathematical_topics_in_quantum_theory
Nonlinear modification of the Schrödinger equation
either the Klein–Gordon equation or the Dirac equation in a curved space-time together with the Einstein field equations. The equation also describes fuzzy
Schrödinger–Newton_equation
Formulation of quantum mechanics
qs. This shows the way in which equation (11) goes over into classical results when h becomes extremely small. — Dirac (1933), p. 69 That is, in the limit
Path-integral_formulation
Partial differential equation describing the evolution of temperature in a region
where δ {\displaystyle \delta } is the Dirac delta function. With a simple division, the Schrödinger equation for a single particle of mass m in the absence
Heat_equation
Quantum mechanical model
method, developed by Paul Dirac, allows extraction of the energy eigenvalues without directly solving the differential equation. It is generalizable to
Quantum_harmonic_oscillator
Elementary particle with negative charge
1928, building on Wolfgang Pauli's work, Paul Dirac produced a model of the electron – the Dirac equation, consistent with relativity theory, by applying
Electron
Value in quantum electrodynamics
result), can be calculated from the Dirac equation. It is usually expressed in terms of the g-factor; the Dirac equation predicts g = − 2 {\displaystyle g=-2}
Anomalous magnetic dipole moment
Anomalous_magnetic_dipole_moment
Material composed of antiparticles
began in 1928, with a paper by Paul Dirac. Dirac realised that his relativistic version of the Schrödinger wave equation for electrons predicted the possibility
Antimatter
Dimensionless number that quantifies the strength of the electromagnetic interaction
This constant was not seen as significant until Paul Dirac's linear relativistic wave equation in 1928, which gave the exact fine structure formula.
Fine-structure_constant
Principle of quantum mechanics
{\displaystyle |1\rangle } denote particular solutions to the Schrödinger equation in Dirac notation weighted by the two probability amplitudes c 0 {\displaystyle
Quantum_superposition
DIRAC EQUATION
DIRAC EQUATION
Boy/Male
Muslim
Old Arabic name
Boy/Male
Muslim
Scholar
Boy/Male
Indian
Scholar
Boy/Male
Indian
Old Arabic name
Girl/Female
Indian
Beautiful, Splendor, Derived from Indira - Goddess laxmis name
Girl/Female
Tamil
Beautiful, Splendor, Derived from Indira - Goddess laxmis name
DIRAC EQUATION
DIRAC EQUATION
Female
English
Feminine form of Old French Norbert, NORBERTA means "bright northman" or "famous northman."
Female
Dutch
, resolute helmet.
Girl/Female
Muslim
Joy. Delight.
Girl/Female
Gujarati, Hindu, Indian, Kannada, Malayalam
Mercifulness
Female
Turkish
Turkish name ESEN means "wind."
Boy/Male
Indian, Sanskrit, Tamil
Delight; Happiness
Girl/Female
Hindu, Indian, Sanskrit
Creator; Leader; Promulgator
Surname or Lastname
English
English : variant of Skerritt.
Boy/Male
Arabic, Australian
Locust; Liberal
Female
Hebrew
(×ֶמֶת) Hebrew name EMET means "truth." The masculine form is spelled Emmet.
DIRAC EQUATION
DIRAC EQUATION
DIRAC EQUATION
DIRAC EQUATION
DIRAC EQUATION
n.
The bringing of any term of an equation from one side over to the other without destroying the equation.
n.
The change, as of an equation or quantity, into another form without altering the value.
n.
Belonging to number; denoting number; consisting in numbers; expressed by numbers, and not letters; as, numerical characters; a numerical equation; a numerical statement.
n.
Either of the two parts of an algebraic equation, connected by the sign of equality.
n.
The system of equations required for the complete expression of the relations which exist between a set of quantities.
n.
An identical equation.
n.
The curve whose ordinates are proportional to the sines of the abscissas, the equation of the curve being y = a sin x. It is also called the curve of sines.
v. t.
To bring, as any term of an equation, from one side over to the other, without destroying the equation; thus, if a + b = c, and we make a = c - b, then b is said to be transposed.
a.
Pertaining to terms of the second degree; as, a quadratic equation, in which the highest power of the unknown quantity is a square.
n.
A spiral whose polar equation is r2/ = a; that is, a curve the square of whose radius vector varies inversely as the angle which the radius vector makes with a given line.
n.
A curve or surface whose equation is of the fourth degree in the variables.
n.
The act of solving, or the state of being solved; the disentanglement of any intricate problem or difficult question; explanation; clearing up; -- used especially in mathematics, either of the process of solving an equation or problem, or the result of the process.
n.
A quantity which may increase or decrease; a quantity which admits of an infinite number of values in the same expression; a variable quantity; as, in the equation x2 - y2 = R2, x and y are variables.
n.
A surface whose equation in three variables is of the second degree. Spheres, spheroids, ellipsoids, paraboloids, hyperboloids, also cones and cylinders with circular bases, are quadrics.
n.
An expression of the condition of equality between two algebraic quantities or sets of quantities, the sign = being placed between them; as, a binomial equation; a quadratic equation; an algebraic equation; a transcendental equation; an exponential equation; a logarithmic equation; a differential equation, etc.
n.
That branch of algebra which treats of quadratic equations.
n.
A curve of the fourth degree, invented by Pascal. Its polar equation is r = a cos / + b.
a.
Recurring once a month; monthly; gone through in a month; as, the menstrual revolution of the moon; pertaining to monthly changes; as, the menstrual equation of the sun's place.
n.
Rank; degree; thus, the order of a curve or surface is the same as the degree of its equation.
n.
A small branching shrub (Dirca palustris), with a white, soft wood, and a tough, leathery bark, common in damp woods in the Northern United States; -- called also moosewood, and wicopy.