TITLE:
Hamilton-Jacobi and Lagrange Formulations of Relativistic Quantum Mechanics Wave Equations with Solutions with Only-Positive and Only-Negative Kinetic Energies
AUTHORS:
Luis Grave de Peralta, Arquímedes Ruiz-Columbie
KEYWORDS:
Quantum Mechanics, Relativistic Quantum Mechanics
JOURNAL NAME:
Journal of Modern Physics,
Vol.13 No.4,
April
21,
2022
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.