Journal of Modern Physics

Hamilton-Jacobi and Lagrange Formulations of Relativistic Quantum Mechanics Wave Equations with Solutions with Only-Positive and Only-Negative Kinetic Energies

Luis Grave de Peralta, Arquímedes Ruiz-Columbié

Published Jan 1, 2022• 0 citations

Abstract

Using the Hamilton-Jacobi and the Lagrange formalisms, a pair of relativistic quantum mechanics equations are obtained by abduction. These equations, in contrast with the Klein-Gordon and other relativistic quantum mechanics equations, have no solutions with both positive and negative kinetic energies. The equation with solutions with only positive kinetic energy values describes a spin-0 particle of mass m, which is moving at relativistic speeds in a scalar potential. The wavefunctions and the energies corresponding to the associated antiparticle can be obtained by solving the other equation, which only has solutions with negative kinetic energy values.

DOI: 10.4236/jmp.2022.134030

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