Avoided level crossings in quasi-exact approach

Abstract

In the quantum models described by analytic potentials V(r) with several pronounced minima the phenomenon of tunneling opens the possibility of a sudden relocalization of the system after a minor modification of parameters. This may really reorder the minima and change, thoroughly, the shape of the (measurable) probability density. In the spectrum one observes the "avoided crossings" of the energy levels. By definition, the relocalization configurations are sensitive to perturbations and represent, therefore, a crossroad to alternative evolution scenarios. As long as the numerical search for these quantum analogues of the Thom's classical catastrophes is not easy, a systematic non-numerical approach is proposed here, based on an exact (or, better, quasi-exact) simultaneous construction of mutually consistent pairs of potentials V(r) and wave functions psi(r). (C) 2021 The Author(s). Published by Elsevier B.V.