About: Dirac equation   Sponge Permalink

An Entity of Type : owl:Thing, within Data Space : 134.155.108.49:8890 associated with source dataset(s)

The equation in the form originally proposed by Dirac is: {|cellpadding="6" style="border:2px solid #0073CF;background: #F5FFFA; text-align: center;" | |} where ψ = ψ(r, t) is a complex four-component field ψ that Dirac thought of as the wave function for the electron, r and t are the space and time coordinates, m is the rest mass of the electron, is the momentum operator, c is the speed of light, and ħ is the reduced Planck constant (h/2π). Furthermore, α is a vector operator whose components are 4 × 4 matricies: α = (α1, α2, α3), and β is another 4 × 4 matrix.

AttributesValues
rdfs:label
  • Dirac equation
rdfs:comment
  • The equation in the form originally proposed by Dirac is: {|cellpadding="6" style="border:2px solid #0073CF;background: #F5FFFA; text-align: center;" | |} where ψ = ψ(r, t) is a complex four-component field ψ that Dirac thought of as the wave function for the electron, r and t are the space and time coordinates, m is the rest mass of the electron, is the momentum operator, c is the speed of light, and ħ is the reduced Planck constant (h/2π). Furthermore, α is a vector operator whose components are 4 × 4 matricies: α = (α1, α2, α3), and β is another 4 × 4 matrix.
sameAs
dcterms:subject
dbkwik:speedydelet...iPageUsesTemplate
border colour
  • #50C878
  • #0073CF
cellpadding
  • 6(xsd:integer)
  • 10(xsd:integer)
Indent
  • :
Background Colour
  • #ECFCF4
  • #F5FFFA
abstract
  • The equation in the form originally proposed by Dirac is: {|cellpadding="6" style="border:2px solid #0073CF;background: #F5FFFA; text-align: center;" | |} where ψ = ψ(r, t) is a complex four-component field ψ that Dirac thought of as the wave function for the electron, r and t are the space and time coordinates, m is the rest mass of the electron, is the momentum operator, c is the speed of light, and ħ is the reduced Planck constant (h/2π). Furthermore, α is a vector operator whose components are 4 × 4 matricies: α = (α1, α2, α3), and β is another 4 × 4 matrix. This single symbolic equation unravels into four coupled linear first-order partial differential equations for the four quantities that make up the field. These matrices, and the form of the field, have a deep mathematical significance. The algebraic structure represented by the Dirac matrices had been created some 50 years earlier by the English mathematician W. K. Clifford. In turn, Clifford's ideas had emerged from the mid-19th century work of the German mathematician Hermann Grassmann in his "Lineale Ausdehnungslehre" (Theory of Linear Extensions). The latter had been regarded as well-nigh incomprehensible by most of his contemporaries. The appearance of something so seemingly abstract, at such a late date, and in such a direct physical manner, is one of the most remarkable chapters in the history of physics. Dirac's purpose in casting this equation was to explain the behavior of the relativistically moving electron, and so to allow the atom to be treated in a manner consistent with relativity. His rather modest hope was that the corrections introduced this way might have bearing on the problem of atomic spectra. Up until that time, attempts to make the old quantum theory of the atom compatible with the theory of relativity by discretizing the angular momentum of the electron's orbit had failed – and the new quantum mechanics of Heisenberg, Pauli, Jordan, Schrödinger, and Dirac himself had not developed sufficiently to treat this problem. Although Dirac's original intentions were satisfied, his equation had far deeper implications for the structure of matter, and introduced new mathematical classes of objects that are now essential elements of fundamental physics.
Alternative Linked Data Views: ODE     Raw Data in: CXML | CSV | RDF ( N-Triples N3/Turtle JSON XML ) | OData ( Atom JSON ) | Microdata ( JSON HTML) | JSON-LD    About   
This material is Open Knowledge   W3C Semantic Web Technology [RDF Data] Valid XHTML + RDFa
OpenLink Virtuoso version 07.20.3217, on Linux (x86_64-pc-linux-gnu), Standard Edition
Data on this page belongs to its respective rights holders.
Virtuoso Faceted Browser Copyright © 2009-2012 OpenLink Software