  We analyze the position and momentum uncertainties of the energy eigenstates
of the harmonic oscillator in the context of a deformed quantum mechanics,
namely, that in which the commutator between the position and momentum
operators is given by [x,p]=i\hbar(1+\beta p^2). This deformed commutation
relation leads to the minimal length uncertainty relation \Delta x >
(\hbar/2)(1/\Delta p +\beta\Delta p), which implies that \Delta x ~ 1/\Delta p
at small \Delta p while \Delta x ~ \Delta p at large \Delta p. We find that the
uncertainties of the energy eigenstates of the normal harmonic oscillator
(m>0), derived in Ref. [1], only populate the \Delta x ~ 1/\Delta p branch. The
other branch, \Delta x ~ \Delta p, is found to be populated by the energy
eigenstates of the `inverted' harmonic oscillator (m<0). The Hilbert space in
the 'inverted' case admits an infinite ladder of positive energy eigenstates
provided that \Delta x_{min} = \hbar\sqrt{\beta} > \sqrt{2}
[\hbar^2/k|m|]^{1/4}. Correspondence with the classical limit is also
discussed.
