  We analyze the supersymmetric features of isolated double-well potentials,
both symmetric ones and ones under an asymmetric perturbation. Our studies are
in concert with results obtained elsewhere. Further on, a particular interest
is paid to double- and single-valley potentials occurring in pairs on applying
the adiabatic approximation to coupled electron-vibrational mode systems. Among
the latter are Holstein's small polarons and the vibronic (off-center)
band-species performing a finite-orbital-momentum helical motion. Our results
seem to revive an earlier assertion for the existence of artifacts in the
adiabatic approximation.
