Nature comes to us with many hierarchies of scale, and science progresses because we do not need to understand them all at once. Effective theories exploit this fact to isolate what is important at any scale. This talk summaries how effective theories work as well as some of their surprising applications to the ordinary quantum mechanics of a particle moving within a potential. Thought of as effective theories these quantum mechanical problems already provide examples of more complicated effects, like renormalization and dimensional transmutation. They also modify how finite-size effects alter bound-state orbits in the Coulomb problem, and in particular indicate a non-standard dependence on the mass of the orbiting particle. It is argued that this might provide a solution to the 'proton-radius puzzle', in which experiments seem to indicate a different radius for the proton depending on whether or not it is being orbited by electrons or muons.