Upper bounds for errors of expectations in the few-body problem

Exact upper bounds are established for the errors associated with approximate computations of total, kinetic, and potential energies of a few-body system. As a consequence, error bounds are also established for arbitrary coordinate functions. Reduction methods are developed to treat expectations of coordinate functions which are divergent at some spatial point, e.g., the delta function or the inverse square, or at infinity, e.g., the mean-square radius. Positronium is used as a test case to study the relative accuracy of the estimates.