Dmitrii Kouznetsov

“ Introduction The simplest quantum-mechanical model of the interaction of an atom with the electromagnetic field field, which still allows the spontaneous decay, was suggested a century ago [3] and then widely applied; in particular, to idealized 3-level systems [4] [5] [1] [2] . The original deduction by Weisscopf and Wigner of the rate of decay (and the resulting spectrum of the emitted photons) is rather euristic than rigorous. The Schroedinger equation for the quantum amplitude with excited atom and that with photons allows the solution in terms of generalized functions. ”

“ In the free space, the mode of a photon may be just a field emitted by a classical dipole. However, in the special case with non-unifom space, for example, an atom trapped in vicinity of a single-mode nanofiber [7] , the mode may have more complicated form. For the process of the elementary decay, the only commutation properties are important:
(3) and all other commutators , , , are equal to zero; in addition, , which means that we have only one atom and it cannot be double-excited. ”

“ In such a way, for the infinite integration in ref (dhdttilde) , the exponential solution for appears as an analytic and exact result, not as a special and limiting case of consideration of some discrete momentum space with an additional physical assumptions. ”