We continue our previous application of supersymmetric quantum mechanical
methods to eigenvalue problems in the context of some deformed canonical
commutation relations leading to nonzero minimal uncertainties in position
and/or momentum. Here we determine for the first time the spectrum and the
eigenvectors of a one-dimensional harmonic oscillator in the presence of a
uniform electric field in terms of the deforming parameters $\alpha$, $\beta$.
We establish that whenever there is a nonzero minimal uncertainty in momentum,
i.e., for $\alpha \ne 0$, the correction to the harmonic oscillator eigenvalues
due to the electric field is level dependent. In the opposite case, i.e., for
$\alpha = 0$, we recover the conventional quantum mechanical picture of an
overall energy-spectrum shift even when there is a nonzero minimum uncertainty
in position, i.e., for $\beta \ne 0$. Then we consider the problem of a
$D$-dimensional harmonic oscillator in the case of isotropic nonzero minimal
uncertainties in the position coordinates, depending on two parameters $\beta$,
$\beta'$. We extend our methods to deal with the corresponding radial equation
in the momentum representation and rederive in a simple way both the spectrum
and the momentum radial wave functions previously found by solving the
differential equation. This opens the way to solving new $D$-dimensional
problems.