  Various theories of quantum gravity predict the existence of a minimum length
scale, which leads to the modification of the standard uncertainty principle to
the Generalized Uncertainty Principle (GUP). In this paper, we study two forms
of the GUP and calculate their implications on the energy of the harmonic
oscillator and the Hydrogen atom more accurately than previous studies. In
addition, we show how the GUP modifies the Lorentz force law and the
time-energy uncertainty principle.
