%0 Journal Article
%T Natural Extension of the Schrödinger Equation to Quasi-Relativistic Speeds
%A Luis Grave de Peralta
%J Journal of Modern Physics
%P 196-213
%@ 2153-120X
%D 2020
%I Scientific Research Publishing
%R 10.4236/jmp.2020.112012
%X A Schr<span style=\"white-space:nowrap;\">&amp;ouml;</span>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<span style=\"white-space:nowrap;\">&amp;ouml;</span>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.
%K Quantum Mechanics
%K Schr&#246
%K dinger Equation
%K Klein-Gordon Equation
%K Relativistic Quantum Mechanics
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=98147