  We apply the ideas of effective field theory to nonrelativistic quantum
mechanics. Utilizing an artificial boundary of ignorance as a calculational
tool, we develop the effective theory using boundary conditions to encode
short-ranged effects that are deliberately not modeled; thus, the boundary
conditions play a role similar to the effective action in field theory.
Unitarity is temporarily violated in this method, but is preserved on average.
As a demonstration of this approach, we consider the Coulomb interaction and
find that this effective quantum mechanics can predict the bound state energies
to very high accuracy with a small number of fitting parameters. It is also
shown to be equivalent to the theory of quantum defects, but derived here using
an effective framework. The method respects electromagnetic gauge invariance
and also can describe decays due to short-ranged interactions, such as those
found in positronium. Effective quantum mechanics appears applicable for
systems that admit analytic long-range descriptions, but whose short-ranged
effects are not reliably or efficiently modeled. Potential applications of this
approach include atomic and condensed matter systems, but it may also provide a
useful perspective for the study of blackholes.
