  We consider a Generalized Uncertainty Principle (GUP) framework which
predicts a maximal uncertainty in momentum and minimal uncertainties both in
position and momentum. We apply supersymmetric quantum mechanics method and the
shape invariance condition to obtain the exact harmonic oscillator eigenvalues
in this GUP context. We find the supersymmetric partner Hamiltonians and show
that the harmonic oscillator belongs to a hierarchy of Hamiltonians with a
shift in momentum representation and different masses and frequencies. We also
study the effect of a uniform electric field on the harmonic oscillator energy
spectrum in this setup.
