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# Topic: Dirac equation

###### In the News (Thu 20 Jun 19)

 Charles Bloom's Page : The Dirac Equation Oh, and I also make a (new to me, anyway) interpretation of the Dirac equation, which is kind of amusing. First, some conventions for this text-based equation writing. All the Dirac equation says is that when you translate into the frame of the particle, the energy equals the mass. www.cbloom.com /physics/dirac.html   (1156 words)

 Dirac equation The Dirac equation is a relativistic quantum mechanical wave equation which describes the behavior of relativistic fermions, invented by Paul Dirac in 1928. For several years the meaning of the Dirac equation was unclear because no one understood the meaning of the negative energy levels that the equation predicted. One of the consequences of the Dirac equation is the prediction of antimatter. www.ebroadcast.com.au /lookup/encyclopedia/di/Dirac_equation.html   (381 words)

 Dirac equation Encyclopedia   (Site not responding. Last check: ) In physics, the Dirac equation is a relativistic quantum mechanical wave equation formulated by British physicist Paul Dirac in 1928 and provides a description of elementary spin-½ particles, such as electrons, consistent with both the principles of quantum mechanics and the theory of special relativity. The equation demands the existence of antiparticles and actually predated their experimental discovery, making the discovery of the positron, the antiparticle of the electron, one of the greatest triumphs of modern theoretical physics. This is the basis for the use of the Dirac equation in quantum field theory. www.hallencyclopedia.com /topic/Dirac_equation.html   (3018 words)

 The Dirac Equation   (Site not responding. Last check: ) Though it is theoretically sound from the perspective that it comes straight from the equations of special relativity, it has several unsavory features which keep it from being a very powerful tool in relativistic quantum mechanics. Dirac later developed his own relativistic wave equation which did not have some of the shortcomings of the Klein-Gordon equation and that some of the supposed errors'' that the KG equation gave rise to were actually illustrating some new physics. The Dirac equation is only rigorous for a one particle system, but has been used as a starting point for a great number of approximate many electron methods. www.uam.es /docencia/quimcursos/Docs/Knowledge/Fundamental_Theory/rltvt/node7.html   (139 words)

 1 The Dirac Equation   (Site not responding. Last check: ) Dirac later developed his own relativistic wave equation which did not have some of the shortcomings of the Klein-Gordon equation. Dirac's formulation also led to the discovery that some of the supposed errors'' of the KG equation were actually illustrating some new physics. The Dirac equation is only rigorous for a one particle system, but has been used as a starting point for a number of approximate many electron methods. zopyros.ccqc.uga.edu /~kellogg/docs/rltvt/node2.html   (151 words)

 [No title]   (Site not responding. Last check: ) Dirac's fame stems from his formulation in 1928 of a mathematical description of elementary particles that accords with both quantum mechanics and the theory of relativity. The Dirac equation was surprising in that it involved matrices (arrays of numbers that may assume different forms for different observers) rather than scalar quantities. Dirac was Lucasian Professor of Mathematics at Cambridge from 1932 to 1969 and professor of physics at Florida State University, from 1971 until his death. www.phy.hr /~dpaar/fizicari/xdirac.html   (269 words)

 The Dirac Equation and the Positron Paul Dirac himself suggested that "one should allow oneself to be led in the direction which the mathematics suggests." It takes a great deal of faith to be led by mathematics which produces some seemingly meaningless results, but that faith led Dirac to a correct relativistic electron equation and the prediction of the positron. Before Dirac invented his equation in 1928 the energy of a particle was modeled by the Shrodinger equation. At the time Dirac came out with his equation no one wanted to, or had the guts to, suggest that there might be a new particle with a positive charge and the mass of an electron. www.phy.duke.edu /~kolena/modern/deaton.html   (901 words)

 Dirac Equation   (Site not responding. Last check: ) The problem that Dirac set out to solve was to find an equation similar to the Schrödinger equation, but which obeys Einstein's special theory of relativity. Dirac then noticed that if he used a whole collection of wave functions, ordered in a matrix, he could construct an equation which was relativistic, but did not have negative probabilities. The Dirac equation is thus regarded as an equation for the evolution of the electron field, just as the Klein-Gordon equation is the evolution equation for a spinless field (such as the Higgs field). www.physto.se /~lbe/enm/diraceq.htm   (573 words)

 Introduction to the Dirac equation In 1928, P.A.M. Dirac proposed a relativistic formulation of the quantum mechanics of the electron from which spin emerges as a natural consequence of the relativistic treatment. Dirac's relativistic formulation of the electron becomes necessary to employ when one is interested in the low lying (core) states of heavy atoms, where, because of the large Coulomb forces ( In addition, Dirac's theory is the basis for modern quantum electrodynamics, one of the most accurate quantum theories to date. www.nyu.edu /classes/tuckerman/quant.mech/lectures/lecture_6/node5.html   (463 words)

 Nonrelativistic Limit of the Dirac Equation This is the two-component Pauli equation for the theory of spin in nonrelativistic quantum mechanics. The Pauli equation, and thus the Dirac equation, yields the correct gyromagnetic factor of Since the Pauli equation is a nonrelativistic wave equation for a spin-1/2 particle, the Dirac equation describes a particle with spin-1/2 both at low and high velocities. www.phys.ualberta.ca /~gingrich/phys512/latex2html2/node46.html   (386 words)

 Dirac equation which is structurally somewhat different from the Schrödinger equation because of the symmetric term depending on the rest mass, and the antisymmetric presence of the kinetic energy in two different places. This is the spherical cosine law for a unit hyperboloid with an angle between edges of the triangle of We don't see such clear bumps on the cosine curves as for the Schrödinger equation, but the result is very similar. delta.cs.cinvestav.mx /~mcintosh/comun/mathieu/node4.html   (249 words)

 The world's top Relativistic websites Dirac was presented by the BBC in January 2004 as a prototype algorithm for the encoding and decoding of raw video and sound to smaller filesizes intended as the basis of a new file format for the transmission of video over the internet. The codec is named in honour of the British scientist Paul Dirac. The experimental, and unfinished codec written in the programming language C++ was released under an Open Source licence at SourceForge on the 11th of March 2004. www.websbiggest.com /dir-wiki.cfm/Top/Science/Physics/Quantum_Mechanics/Relativistic   (270 words)

 The Dirac equation The Dirac Hamiltonian for a spin ½ particle in the presence of an electromagnetic field is The first and third term give the non relativistic Schroedinger equation, the second term has the form of the classical relativistic correction, the last term is the spin-orbit energy, which appears as an automatic consequence of the Dirac equation. The fourth term is a similar relativistic correction to the potential energy, which does not have a classical analog. electron6.phys.utk.edu /qm2/modules/m9/dirac.htm   (423 words)

 Abstract - Stochastic Processes and the Dirac Equation with External Fields Abstract - Stochastic Processes and the Dirac Equation with External Fields Stochastic Processes and the Dirac Equation with External Fields The equation describing the stochastic motion of a classical particle in 1+1-dimensional space-time is connected to the Dirac equation with external gauge fields. cola.kaist.ac.kr /abstract/2002071.htm   (100 words)

 SciRate.com In $t$-scale, the Schr$\ddot{\rm o}$dinger equation holds and for a macrovariable just a classical path is picked up as a peak of $\Psi$ by the stationary phase, which is the observable signal. A Markovian dynamical equation is introduced without relying on the rotating wave approximation in the system-external field interaction. We show that the time evolution of the two-level system is directed towards an incoherent sum of periodic Floquet states regardless of the initial state and even the type of the coupling to the environment. scirate.com   (2141 words)

 Relativistic Quantum Mechanics (by Walter Pfeifer) This book deals mainly with the Dirac equation, its properties, its applications and its limiting cases. A formalism for particles with arbitrary spin and remarks on other relativistic quantum mechanical equations are given. From the contents: The Lorentz transformation, quantum mechanical operators, the Dirac equation, probability density, nonrelativistic limits of the Dirac equation, anomalous magnetic moment, free particle, cyclotron motion, parity, total angular momentum, Dirac particle in a Coulomb field, massless particles, particles with arbitrary spin, charge conjugation, the Klein-Gordon equation. www.walterpfeifer.ch /relqm   (262 words)

 Energy Citations Database (ECD) - - Document #482188 We present new procedures in the REDUCE language for algebraic programming of the Dirac equation on curved space-time. The main part of the program is a package of routines defining the Pauli and Dirac matrix algebras. Then the Dirac equation is obtained using the facilities of the EXCALC package. www.osti.gov /energycitations/product.biblio.jsp?osti_id=482188&query_id=0   (206 words)

 Series Solutions For The Dirac Equation In Kerr Newman Space Time (ResearchIndex) If your firewall is blocking outgoing connections to port 3125, you can use these links to download local copies. Abstract: The Dirac equation is solved for an electron in a Kerr Newman geometry using an adaptation of the procedure of Chandrasekhar. The corresponding eigenfunctions obtained can be represented as series of Jacobi polynomials. citeseer.ist.psu.edu /467128.html   (392 words)

 Viktor's Home Page: Physics notes is not Einstein's Equation (August 13, 2004): I recently saw an article that "exposed" Einstein as a "fraud" whose "derivation" of The Principle of Least Action (July 22, 2004): deriving the equation of motion in an electrostatic field Quaternions and the Dirac Equation (Mar 13, 2003): an attempt to reformulate what I know about the Dirac equation using quaternion algebra www.vttoth.com /physics.htm   (690 words)

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