Article

    Ufa Mathematical Journal
    Volume 3, Number 4, pp. 13-19

    Asimptotic presentation of eigenfunctions of the two-dimensional harmonic oscillator


    Akhmerova E.F.

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    In this work has been obtained the asymptotic of the eigen-\linebreak functions of the two-dimensional harmonic oscillator all over the a space. The need of such presentation arises at the moment of studying the spectral characteristics no compact perturbation of the two-dimensional harmonic oscillator. The absence of exact asimptotic equality for funda-\linebreak mental systems solution of the differential equation complicates the study, because eigenfunctions of the two-dimensional harmonic oscillator have the image of the composition of normalize eigenfunctions of the one-dimensional harmonic oscillator. The usage of comparison solutions helps to decide this problem.