Relativistic Wave Equation for Spin-O Particles The Klein-Gordon Equation and Its Applications

  • Walter Greiner


The description of phenomena at high energies requires the investigation of relativistic wave equations. This means equations which are invariant under Lorentz transformations. The transition from a nonrelativistic to a relativistic description implies that several concepts of the nonrelativistic theory have to be reinvestigated, in particular:
  1. 1)

    Spatial and temporal coordinates have to be treated equally within the theory.

  2. 2)
    $$ \Delta x \sim \frac{\hbar }{{\Delta p}} \sim \frac{\hbar }{{m_\text{0} c}} $$
    , a relativistic particle cannot be localized more accurately than ≈ ħ/m 0 c; otherwise pair creation occurs for E > 2m 0 c 2. Thus, the idea of a free particle only makes sense, if the particle is not confined by external constraints to a volume which is smaller than approximately the Compton wavelength λc = ħ/m 0 c. Otherwise the particle automatically has companions due to particle-antiparticle creation.


Wave Function Lorentz Transformation Neutral Particle Lagrange Density Energy Eigenvalue 
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  1. 1.
    We adopt the same notation as J. D. Bjorken, S. D. Drell: Relativistic Quantum Mechanics(McGraw Hill, New York 1964).Google Scholar
  2. 3.
    See H. Goldstein: Classical Mechanics, 2nd ed. (Addison- Wesley, Reading, MA 1980)MATHGoogle Scholar
  3. W. Greiner: Theoretische Physik II: Mechanik II(Hairy Deutsch, Frankfurt a.m. 1989).Google Scholar
  4. 4.
    See J. D. Jackson: Classical Electrodynamics, 2nd ed. (Wiley, New York 1975).Google Scholar
  5. 5.
    See Example 1.3 and, for a detailed discussion, J.D. Jackson: Classical Electrodynamics, 2nd ed. (Wiley, New York 1975)Google Scholar
  6. W. Greiner: Theoretische Physik UI, Klassische Elektrodynamik(Hairy Deutsch, Frankfurt a.M. 1985).Google Scholar
  7. 15.
    See M. Abramowitz, I.A. Stegun: Handbook of Mathematical Functions(Dover, New York 1965), p. 438.Google Scholar
  8. M. Abramowitz, LA. Stegun: Handbook of Mathematical Functions(Dover, New York 1965).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1990

Authors and Affiliations

  • Walter Greiner
    • 1
  1. 1.Institut für Theoretische PhysikJohann Wolfgang Goethe-Universität FrankfurtFrankfurt am MainGermany

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