Asymptotic presentation of eigenfunctions of a two-dimensional harmonic oscillator
The asymptotics of eigenfunctions of a two-dimensional harmonic oscillator has been obtained all over the space. The need of such presentation arises when studying the spectral characteristics of non compact perturbation of the twodimensional harmonic oscillator. The absence of exact asymptotic equalities for fundamental systems of solutions to the differential equation complicates the study, because eigenfunctions of the two-dimensional harmonic oscillator are represented in the form of a product of normalized eigenfunctions of the one-dimensional harmonic oscillator. The usage of standard solutions helps to solve the problem.