Summary: Let \(\ell(y) = y'' + qy\), where \(q\) is a positive, continuously differentiable function defined on a ray \([a,\infty)\). The operator \(\ell\) determines, with appropriate restrictions, self-adjoint operators defined in the Hilbert space \(\mathcal L_2[a,\infty)\) of quadratically summable, complex-valued functions on \([a,\infty)\). In this note, we prove that if \(L\) is such a self-adjoint operator, then the conditions \(q(t)\to\infty\) and \(q'(t)q(t)^{-1/2}\to 0\) as \(t\to\infty\) are sufficient for the continuous spectrum \(C(L)\) of \(L\) to cover the entire real axis.