Natural Extension of the Schrödinger Equation to Quasi-Relativistic Speeds

Author: Luis Grave de Peralta

ABSTRACT
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.

Source:

Journal: Journal of Modern Physics
DOI: 10.4236/jmp.2020.112012 (PDF)
Paper Id: 98147 (metadata)

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