The stationary Schr$\stackrel{..}{o}$dinger equation for an oscillator with perturbation $\lambda x^{-2}$ has been revised. A new choice of even states of the singular oscillator is made based on the automodel requirement for the solution to the Schrodinger equation for a free particle with the same perturbation. In contrast to the orthodox solution, the suggested solution provides alternation of even and odd levels and the stability of the ground state, and consequently, is physically preferable.
Department of Theoretical Physics, Faculty of Physics, Moscow State University, Leninskie Gory, Moscow, 119992, Russi
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