Author(s)

Luis Grave de Peralta^1,2*, Arquímedes Ruiz-Columbie³

¹Department of Physics and Astronomy, Texas Tech University, Lubbock, TX, USA.
²Nano Tech Center, Texas Tech University, Lubbock, TX, USA.
³Wind Energy Program, Texas Tech University, Lubbock, TX, USA.

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.

Quantum Mechanics, Relativistic Quantum Mechanics

de Peralta, L. and Ruiz-Columbie, A. (2022) Hamilton-Jacobi and Lagrange Formulations of Relativistic Quantum Mechanics Wave Equations with Solutions with Only-Positive and Only-Negative Kinetic Energies. Journal of Modern Physics, 13, 432-441. doi: 10.4236/jmp.2022.134030.