Natural Extension of the Schrödinger Equation to Quasi-Relativistic Speeds

Author: Luis Grave de Peralta

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.


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

See also: Comments to Paper

About scirp

(SCIRP: is an academic publisher of open access journals. It also publishes academic books and conference proceedings. SCIRP currently has more than 200 open access journals in the areas of science, technology and medicine. Readers can download papers for free and enjoy reuse rights based on a Creative Commons license. Authors hold copyright with no restrictions. SCIRP calculates different metrics on article and journal level. Citations of published papers are shown based on Google Scholar and CrossRef. Most of our journals have been indexed by several world class databases. All papers are archived by PORTICO to guarantee their availability for centuries to come.
This entry was posted in JMP. Bookmark the permalink.

Leave a Reply

Your email address will not be published. Required fields are marked *