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In this article it is shown that, Sommerfeld's coefficients for excitonictransitions in quantum wells are determined only with the principle quantumnumber within the framework of two-dimensional Coulomb potential. This is aconsequence of hidden symmetry of two-dimensional Coulomb problem, conditionedby the existence of two-dimensional analog of the Runge-Lentz vector. For thenarrow gap semiconductor quantum well with the non-parabolic dispersion law ofelectron and hole in the two-band Kane model it is shown that two-dimensionalexcitonic states are described in the frames of an analog of Klein-Gordonequation with the two-dimensional Coulomb potential. The non-stability of theground state of the two-dimensional Kane's exciton is show.

Hidden Symmetry, Excitonic Transitions and Two-Dimensional Kane's Exciton in the Quantum Well