  We show that the existence of a minimum measurable length and the related
Generalized Uncertainty Principle (GUP), predicted by theories of Quantum
Gravity, influence all quantum Hamiltonians. Thus, they predict quantum gravity
corrections to various quantum phenomena. We compute such corrections to the
Lamb Shift, the Landau levels and the tunnelling current in a Scanning
Tunnelling Microscope (STM). We show that these corrections can be interpreted
in two ways: (a) either that they are exceedingly small, beyond the reach of
current experiments, or (b) that they predict upper bounds on the quantum
gravity parameter in the GUP, compatible with experiments at the electroweak
scale. Thus, more accurate measurements in the future should either be able to
test these predictions, or further tighten the above bounds and predict an
intermediate length scale, between the electroweak and the Planck scale.
