In a concise, but accessible for the first acquaintance form the procedure for the quantization of linear oscillator is set out. By analogy with this procedure the procedure of quantization (second quantization) of classical Maxwell’s electrodynamics is set up. The physical sense of the wave functions arguments of transverse electromagnetic field and its Fourier transformation is set up. One pay attention as for quantum coherent (almost a classic) states of the electromagnetic field and for photonics Fock states. Attention is drawn to the fact of absence the power of the universal content of such concepts as field amplitude, phase and number of particles (photons), which are used by experimenter’s to describe the states of a quantized field. The semi quantitative description the interaction processes of a quantum electromagnetic field with substance is set up. Specified situations are shown in which the discrepancy between the predictions of classical and quantum electrodynamics is noticeable at the macroscopic level. 1. de Broglie, L. Waves and quanta. Selected scientific works. M: Logos, Vol.1, 2010.
2. Greenstein George, Zajonc Arthur G. The Quantum Challenge (Modern Research on the Foundations of Quantum Mecanics). JONES AND BARTLETT PUBLISHERS. BOSTON, TORONTO, LONDON, SINGAPORE. 2006.
3. Rodney Loudon. The Quantum Theory of Light. Clrendon Press, Oxford 1973.
4. Landau L.D. & Lifshitz E.M. The Classical Theory of Fields (Volume 2 of A Course of Theoretical Physics) Pergamon Press, 1971.
5. THE QUANTUM THEORY OF RADIATION by W.HEITLER. Oxford at the Clarendon Press, 1954.
6. Veklenko B.A. The breaking of Fresnel’s formula by reflection of resonant radiation from excited media. Applied Physics (Russian) 2011, № 1, pp. 5–14.
7. Klauder J.R. and Sudarshan E.C.G. Fundaments of Quantum Optics// Syracuse University, New York, Amsterdam 1968.

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• classical electrodynamics
• quantum electrodynamics
• quantum coherent states
• Fock states
• photon