  In this paper, we will propose the most general form of the deformation of
Heisenberg algebra motivated by the generalized uncertainty principle. This
deformation of the Heisenberg algebra will deform all quantum mechanical
systems. The form of the generalized uncertainty principle used to motivate
these results will be motivated by space fractional quantum mechanics and
non-locality in quantum mechanical systems. We also analyse a specific limit of
this generalized deformation for one dimensional system, and in that limit, a
nonlocal deformation of the momentum operator generates a local deformation of
all one dimensional quantum mechanical systems. We analyse the low energy
effects of this deformation on a harmonic oscillator, Landau levels, Lamb
shift, and potential barrier. We also demonstrate that this deformation leads
to a discretization of space.
