  Almost all theories of Quantum Gravity predict modifications of the
Heisenberg Uncertainty Principle near the Planck scale to a so-called
Generalized Uncertainty Principle (GUP). Recently it was shown that the GUP
gives rise to corrections to the Schrodinger and Dirac equations, which in turn
affect all non-relativistic and relativistic quantum Hamiltonians. In this
paper, we apply it to superconductivity and the quantum Hall effect and compute
Planck scale corrections. We also show that Planck scale effects may account
for a (small) part of the anomalous magnetic moment of the muon. We obtain
(weak) empirical bounds on the undetermined GUP parameter from present-day
experiments.
