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Hamilton-Jacobi and Lagrange Formulations of Relativistic Quantum Mechanics Wave Equations with Solutions with Only-Positive and Only-Negative Kinetic Energies
Department of Physics and Astronomy, Texas Tech University, Lubbock, TX, USA
Wind Energy Program, Texas Tech University, Lubbock, TX, USA
Nano Tech Center, Texas Tech University, Lubbock, TX, USA
- 1 Department of Physics and Astronomy, Texas Tech University, Lubbock, TX, USA
- 2 Wind Energy Program, Texas Tech University, Lubbock, TX, USA
- 3 Nano Tech Center, Texas Tech University, Lubbock, TX, USA
Journal of Modern Physics·Volume 13 (2022)·Pages 432–441·Published 2 April 2022·DOI10.4236/jmp.2022.134030
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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.
KeywordsQuantum MechanicsRelativistic Quantum Mechanics
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