  We study the question of existence and the number of normalized vacuum states
in N = 4 super-Yang-Mills quantum mechanics for any gauge group. The mass
deformation method is the simplest and clearest one. It allowed us to calculate
the number of normalized vacuum states for all gauge groups. For all unitary
groups, #(vac) = 1, but for the symplectic groups [starting from Sp(6) ], for
the orthogonal groups [starting from SO(8)] and for all the exceptional groups,
it is greater than one. We also discuss at length the functional integral
method. We calculate the ``deficit term'' for some non-unitary groups and
predict the value of the integral giving the ``principal contribution''. The
issues like the Born-Oppenheimer procedure to derive the effective theory and
the manifestation of the localized vacua for the asymptotic effective wave
functions are also discussed.
