  Quantum particle is considered confined in a toy-model potential possessing
multiple minima. For the specific choice of the family of potentials (in the
form of harmonic oscillator plus several logarithmic infinitely high but
penetrable barriers), a facilitated tractability of the related bound-state
problem is achieved by the use of the (slightly modified) large-N expansion
technique. The phenomenological appeal of the possibility of simulation of a
certain `relocalization' quantum catastrophe is emphasized.
