Schrödinger-Like Relativistic Wave Equation of Motion for the Lorentz-Scalar Potential

Abstract

A Schrödinger-like relativistic wave equation of motion for the Lorentz-scalar potential is formulated based on a Lagrangian formalism of relativistic mechanics with a scaled time as the evolution parameter. Applications of this Schrödinger-like formalism for the Lorentz-scalar potential are given: For the square-step potential, the predictions of this formalism are free from the Klein paradox, and for the Coulomb potential, this formalism yields the exact bound-state eigenenergies and eigenfunctions.

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Huang, YS. Schrödinger-Like Relativistic Wave Equation of Motion for the Lorentz-Scalar Potential. Foundations of Physics 31, 1287–1298 (2001). https://doi.org/10.1023/A:1012270110871

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Keywords

  • Wave Equation
  • Coulomb Potential
  • Lagrangian Formalism
  • Relativistic Mechanic
  • Evolution Parameter