Author(s)

Luis Grave de Peralta^1,2

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

A Schrödinger-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 Schrödinger 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.

Quantum Mechanics, Schrödinger Equation, Klein-Gordon Equation, Relativistic Quantum Mechanics

Grave de Peralta, L. (2020) Natural Extension of the Schrödinger Equation to Quasi-Relativistic Speeds. Journal of Modern Physics, 11, 196-213. doi: 10.4236/jmp.2020.112012.