Title Church's thesis meets quantum mechanics Author Warren D. Smith SHORTER abstract (not as long as my outrageously long real abstract): I show that garden-variety quantum mechanics (Schr\"odinger equation for $N$ point masses interacting Coulombically) is algorithmically simulable. This extends previous nonalgorithmic work by T.Kato showing existence and uniqueness of solutions, and also previous work by myself showing the same problem for classical mechanics (Newton laws) is {\em not} algorithmically simulable. It also ``proves Church's thesis.'' The simulation algorithm, in a sense I define, exhibits only ``polynomial slowdown'' versus the actual physics, if that simulation is run on a ``quantum computer.'' If run on a conventional computer, it exhibits only ``polynomial memory expansion'' and in a sense is ``quasipolynomial time.'' I also show the spectral energies of quantum bound systems form a computable real sequence. Keywords Church's thesis, quantum $N$-body problem, rigorous physics, uncertainty principle, quantum computers, Feynman path integrals, symplectic integration, exponential splitting formulas, Trotter product formula, BQP, Rayleigh Ritz variational method, computable real numbers, operator computability theory, potential singularities, Coulomb's law, analyticity.