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.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

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 ?
He published his research on the "Extended Dirac Equation for Elementary Fermions based on Applying 8-Dimensional Spinors." DOI: 10.13140/RG.2.2.23994.90569
The Dirac equation (1) can be re-written in the traditional Schrodinger formulation as (H[psi] = E[psi]) where H and E are the energy and Hamiltonian operators respectively.
Groups are usually introduced relatively late in physics education, he admits, but he begins with them in order to arrive at a semblance of the Dirac equation. Then he introduces the very essence of elementary quantum theory to obtain the actual Dirac equation, which governs the motions of the quarks and leptons of the Standard Model.
The Three-Dimensional Dirac Equation for a Free Structure
Just like in the scalar field case, the ambiguity in the quantization can be seen to lie in the choice of a so-called complex structure in the space of solutions (of the Dirac equation in this case).
Nishina succeeded to derive the famous Klein--Nishina formula, (8,9) calculating the intensity distribution of the scattered wave in the Compton scattering based on the Dirac equation. The Klein--Nishina formula has been firmly accepted and widely used, even now.
Hassanabadi, Dirac equation for the Hulthen potential within the Yukawa-type tensor interaction, Chin.
It is well known that the Dirac equation plays a fundamental role in relativistic quantum physics .
Then, we show that this equation is equivalent to the corresponding Dirac equation with an additional condition on the norm of the spinor field (see Proposition 4.1 and Corollary 4.2).
In Section 2, we give a brief description about the Dirac equation and its solution on a circle.
The supersymmetric Dirac equation; the application to hydrogenic atoms.

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