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Natural Extension of the Schrödinger Equation to Quasi-Relativistic Speeds
Department of Physics and Astronomy, 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 Nano Tech Center, Texas Tech University, Lubbock, TX, USA
Journal of Modern Physics·Volume 11 (2020)·Pages 196–213·Published 17 January 2020·DOI10.4236/jmp.2020.112012
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Abstract
A Schr ö dinger-like equation for a single free quantum particle is presented. It is argued that this equation can be considered a natural relativistic extension of the Schr ö dinger equation for energies smaller than the energy associated to the particle’s mass. Some basic properties of this equation: Galilean invariance, probability density, and relation to the Klein-Gordon equation are discussed. The scholastic value of the proposed Grave de Peralta equation is illustrated by finding precise quasi-relativistic solutions for the infinite rectangular well and the quantum rotor problems. Consequences of the non-linearity of the proposed equation for the quantum superposition principle are discussed.
KeywordsQuantum MechanicsSchrödinger EquationKlein-Gordon EquationRelativistic Quantum Mechanics
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