Hamilton-Jacobi and Lagrange formulation of relativistic quantum mechanics wave equations with solutions with only-positive and only-negative kinetic energies

Luis Grave de Peralta, Arquímedes Ruiz-Columbié

Published Feb 18, 2022• 0 citations

Abstract

Abstract Using the Hamilton-Jacobi and the Lagrange formalisms, a pair of relativistic quantum mechanics equations are obtained. 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: 10.21203/rs.3.rs-1332654/v1

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