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

Abstract

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

• 2) Since

  $$ \Delta x \sim \frac{\hbar }{{\Delta p}} \sim \frac{\hbar }{{m_\text{0} c}} $$

  , 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 λ_c = ħ/m ₀ c. Otherwise the particle automatically has companions due to particle-antiparticle creation.