Helmholtz equation in relativistic quantum mechanics

It is shown that for a specific choice of a particular solution of the relativistic wave equation, it falls into the Helmholtz equation and the Klein-Gordon equation. In this case, the squares of the rest masses of the particle with the relativistic dispersion relation are determined by the Helmholtz equation. It suggested the possibility, in principle, of classification of the mass spectrum and lifetimes of the particles according to the discrete solutions of the Helmholtz equation in a particular model. In this case, it can be assumed that the lifetime of a particle is determined by the ratio of contributions to the wave function of the Bessel and collapsed Neumann functions. An opportunity to compare real elementary particles' rest masses and especially lifetimes with the particles' masses and lifetimes considered is discussed.