$$\label{eq:dot2}
h={\vec{p}^2\over m}+ K r^2+\lambda v(r)~,$$ If $v(r)$ is attractive or, at least, has attractive parts, $\lambda v(r)$ will support bound states for large enough $\lambda$. The same phenomenon of level rearrangement is observed, as shown in the simple example of harmonic oscillator and square well. As for the case of exotic atoms, the effect of “level repulsion” is observed, that ovoids any crossing of trajectories corresponding to the same orbital momentum.

Dependence upon the radial number
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As for the theory, it is similar to that of exotic atoms. The analogue of the Trueman–Deser formula, for any long-range potential combined with a short-rangfe potential, reads $$\label{eq:dot3}
\delta E_n \simeq 4\pi a\,|\phi_n(0)|^2 ~,$$ indicating that the energy shift is proportional to the square of the value at the origin of the wave function of the pure long-range potential. It is worth pointing that the dependence upon the radial number $n$ is different for the Coulomb and the oscillator problems:

-   For a narrow pocket of attraction added to an harmonic confinement, the energy shifts at large $n$ increase as $n^{1/2}$, since the square of the wave function at the origin is $|\phi_n(0)|^2=8/[\sqrt{\pi}B(n+1,1/2)]$, where $B$ is the beta function. But for 