  This article is concerned with a special class of the ``double-well-like''
potentials that occur naturally in the analysis of finite quantum systems.
Special attention is paid, in particular, to the so-called Fokker-Planck
potential, which has a particular property: the perturbation series for the
ground-state energy vanishes to all orders in the coupling parameter, but the
actual ground-state energy is positive and dominated by instanton
configurations of the form exp(-a/g), where a is the instanton action. The
instanton effects are most naturally taken into account within the modified
Bohr-Sommerfeld quantization conditions whose expansion leads to the
generalized perturbative expansions (so-called resurgent expansions) for the
energy values of the Fokker-Planck potential. Until now, these resurgent
expansions have been mainly applied for small values of coupling parameter g,
while much less attention has been paid to the strong-coupling regime. In this
contribution, we compare the energy values, obtained by directly resumming
generalized Bohr-Sommerfeld quantization conditions, to the strong-coupling
expansion, for which we determine the first few expansion coefficients in
powers of g^(-2/3). Detailed calculations are performed for a wide range of
coupling parameters g and indicate a considerable overlap between the regions
of validity of the weak-coupling resurgent series and of the strong-coupling
expansion. Apart from the analysis of the energy spectrum of the Fokker-Planck
Hamiltonian, we also briefly discuss the computation of its eigenfunctions.
These eigenfunctions may be utilized for the numerical integration of the
(single-particle) time-dependent Schroedinger equation and, hence, for studying
the dynamical evolution of the wavepackets in the double-well-like potentials.
