In this paper we study the properties of the spectrum of the boundary-value problem $$ \varphi''+[\lambda-x^2-V(x)]\varphi=0,\quad-\infty<x<\infty. $$ Let $\lambda_k$ be the points of the spectrum of this problem, arranged in order of increasing absolute value. Our main result is Theorem. {\it Let $V(x)$ satisfy the conditions $$ |V(x)|\leqslant M,\quad|x|\leqslant L;\qquad|V(x)|\leqslant\frac M{|x|},\quad|x|>L. $$ Then for any $\varepsilon>0$ $$ |\lambda_k-2k-1|=o(k^{-1/2+\varepsilon})\ \text{for}\ k\to\infty. $$} Bibliography: 2 titles.