  In this note we summarize some of the properties found in several papers. We
characterize spectral properties of the quantum mechanical hamiltonian of
theories with fermionic degrees of freedom beyond semiclassical approximation.
We obtain a general class of bosonic polynomial potentials for which the
Schr\"oedinger operator has a discrete spectrum. This class includes all the
scalar potentials in membrane, 5-brane, p-branes, multiple M2 branes, BLG and
ABJM theories. We also give a sufficient condition for discreteness of the
spectrum for supersymmmetric and non supersymmetric theories with a fermionic
contribution. We characterize then the spectral properties of different
theories: the BMN matrix model, the supermembrane with central charges and a
bound state of $N$ D2 with $m$ D0. We show that, while the first two models
have a purely discrete spectrum with finite multiplicity, the latter has a
continuous spectrum starting from a constant given in terms of the monopole
charge.
