Abstract: The discrete emission spectrum of the hydrogen atom is described within a new variation principle of an open physical system in a finite rage of space. Since the electromagnetic field is a non-conservative field the discrete spectra of atoms does not correspond to a quantization of the energy of the particle system and to the quantization of the electromagnetic field with photons. The difference compared with the Schrödinger eigenvalue problem will be considered. The excited atom is, within the Lagrange theory, only a part of the complete system and appears as “resonator” with discrete frequencies ν. The oscillated charge density of the atom radiates classically electromagnetic waves with the wavelengths λ=c/ν and creates the discrete spectra in a finite space-time region. The wave nature of radiation dominates in the atomic emission processes because the wavelengths of the emitted rays are much greater than the sizes of the objects. The “light quantum hypothesis” of quantum mechanics is in our theory replaced with a new variation principle. Furthermore, as the variation principle describes not only bound states but also decaying ones of a system, we can e.g. consider the stable and the unstable particles in a unified way.
PACS numbers: 04.40.Nr, 31.10.+z, 31.15.-p, 32.80.-t