# Dirac Equation

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## Dirac equation

[di′rak i′kwā·zhən]
(quantum mechanics)
A relativistic wave equation for an electron in an electromagnetic field, in which the wave function has four components corresponding to four internal states specified by a two-valued spin coordinate and an energy coordinate which can have a positive or negative value.

## Dirac Equation

a quantum equation for the motion of an electron, meeting the requirements of the theory of relativity; established by Dirac in 1928. It follows from the Dirac equation that an electron has a characteristic mechanical moment of angular momentum—spin—equal to ħ/2 and a characteristic magnetic moment equal to the Bohr magneton /2mc, which were previously (1925) discovered experimentally (e and m are the charge and mass of the electron, c is the velocity of light, and ħ is Planck’s constant). The Dirac equation has made it possible to obtain a more accurate formula of the energy levels of hydrogen and hydrogen-like atoms, which includes the fine structure of the levels; it has also helped explain the Zeeman effect. With the Dirac equation as the basis, formulas have been obtained for the probabilities of scattering photons by free electrons (Compton effect) and radiation emitted by a decelerating electron (bremstrahlung); these formulas have been experimentally confirmed. However, a systematic relativistic description of the motion of an electron is provided by quantum electro-dynamics.

A characteristic feature of the Dirac equation is that its solutions include those that correspond to negative values of energy for the free motion of a particle (corresponding to the negative mass of a particle). This presented a difficulty for the theory, since all the mechanical laws for a particle in such states would be incorrect, although transitions in such states are possible in quantum theory. The real physical sense of transitions to a negative energy level were elucidated later, when the possibility of particle interconversion was proved. It followed from the Dirac equation that a new particle must exist (an antiparticle with respect to the electron) with the mass of an electron and a positive charge: in 1932 such a particle was actually discovered by C. D. Anderson and called the positron. This was a great success for the Dirac theory of the electron. The passage of an electron from a state of negative energy to one of positive energy and the reverse are interpreted as the process of the formation of an electron-positron pair and the annihilation of such a pair.

The Dirac equation is also valid for particles with spin ½ (in ħ units)—mu-mesons and the neutrino. With the proton and neutron, which also have spin ½, it leads to incorrect values of the magnetic moments. The magnetic moment for the Dirac proton should be equal to the nuclear magneton /2Mc (m is the mass of the proton) and that of the neutron to zero since it is uncharged. Experiments show that the magnetic moment of the proton is about 2.8 mangetons and the magnetic moment of the neutron is negative, with an absolute value equal to about two-thirds of the magnetic moment of a proton. The anomalous magnetic moments of these particles are due to their strong interactions.

### REFERENCE

Broglie, L. de. Magnitnyi elektron. Kharkov, 1936. (Translated from French.)
References in periodicals archive ?
The Dirac equation, despite being one of the basic equations of Mathematical Physics, is very poorly understood from an analytical point of view.
and a free fermion [psi](t, x) satisfies the Dirac equation
His topics include from solar systems to atoms, interpretation of the quantum rules, non-relativistic hydrogenic atoms with spin, the primary supersymmetry of the Dirac equation, and a different extension of the solution space.
Such oversights include: the Double Slit Experiment never has been interpreted accurately, as the methods used by physicists to conduct that experiment failed to hold the variable momentum constant; the Dirac equation attempted to unify relativity and quantum mechanics 80 years ago, but never has been interpreted correctly by physicists as the key to the unification of physics; the pictorial claims of matter and antimatter are illogical, given that oppositely charged particles should be attracted to each other rather than repelled; and a discussion of the real problem with siring theory.
These two waves are a Dirac spinor satisfying the Dirac Equation.
The diffusive nature of this equation is problematic but vanishes in the relativistic limit of the Dirac equation.
This is the famous "half-integral spin" term first usually derived from the Dirac equation.
i] and [less than or equal to] i [less than or equal to] 3 obey the Dirac equation but O [intersection] H, q [intersection] q', [q.
After a brief introduction to classical relativity and electromagnetism, the Dirac equation is presented, and its symmetry, atomic solutions, and interpretation are explored.
The proton and electron are Dirac particles in the sense that they both possess a Compton radius and they both obey the Dirac equation, but the positive and negative charge of the proton and electron make their characteristics radically different.
The Electron and Proton Planck-Vacuum Forces and the Dirac Equation.
The Dirac equation is interesting as a spinor construction with no explicit metric but an algebra of gamma-matrices that induce the Minkowskii geometry and causal structure.

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