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I show that we can avoid the paradoxes connected with the wave-particle duality if we consider some classical wave field - “an electron wave” - instead of electrons as the particles and consider the wave equations (Dirac, Schrödinger etc.) as the field equations similar to Maxwell equations for the electromagnetic field. It is shown that the double-slit experiment, the Born rule, the Heisenberg uncertainty principle, the Compton effect etc. all have a simple explanation within classical field theory. It is shown that all of the basic properties of the hydrogen atom can be consistently described in terms of classical electrodynamics. In the framework of classical electrodynamics, the nonlinear Schrödinger equation is obtained, which completely describes the spontaneous emissions of an atom. I show that three well-known laws of the photoelectric effect can be derived within classical field theory. The Planck’s law for the spectral energy density of thermal radiation and the Einstein A-coefficient for spontaneous emission are derived in the framework of classical field theory without using the concept of “photon” and “electron”. These results show that quantum mechanics must be considered to be not a theory of particles but a classical field theory in the spirit of classical electrodynamics.