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

Description

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.

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