We study the effects of loop quantum gravity motivated corrections in classical systems. Computational methods are used to simulate black hole formation from the gravitational collapse of a massless scalar field in Painleve-Gullstrand coordinates. Singularities present in the classical case are resolved by a radiation-like phase in the quantum collapse. The evaporation is not complete but leaves behind an outward moving shell of mass that disperses to infinity. We reproduce Choptuik scaling showing the usual behaviour for the curvature scaling, while observing previously unseen behaviour in the mass scaling. The quantum corrections are found to impose a lower limit on black hole mass and generate a new universal power law scaling relationship. In a parallel study, we quantize the Hamiltonian for a particle in the singular $1/r^2$ potential, a form that appears frequently in black hole physics. In addition to conventional Schrodinger methods, the quantization is performed using full and semiclassical polymerization. The various quantization schemes are in excellent agreement for the highly excited states but differ for the low-lying states, and the polymer spectrum is bounded below even when the Schrodinger spectrum is not.