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

V N Salomatov (1)

1 Irkutsk State Railway University

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.

Mots clés: Relativistic particle; Helmholtz equation; Principle of correspondence

Domaines: Physique [physics]; Physique Quantique [quant-ph]

V N Salomatov. Klein-Gordon and Schrödinger equations for a free particle in the rest frame. 2019. ⟨hal-02336564⟩