Klein-Gordon and Schrödinger equations for a free particle in the rest frame

Published: 28-10-2019| Version 1 | DOI: 10.17632/sbtb359py8.1
Vladimir Salomatov


A system of two equations is found that has solutions which coincide with the solutions of the Klein-Gordon equation in the rest frame. This system includes the Schrödinger equation for a free neutral spinless particle. Using the Schrödinger equation as an additional condition for solving the Klein-Gordon equation in the rest frame leads to two Helmholtz equations. Helmholtz equations can be solved by specifying a particle model and boundary conditions. One of the Helmholtz equations leads to discreteness of the rest masses of relativistic particles.