Error Bounds for Approximations to Expectation Values of Unbounded Operators

A bound for |(BΨ, Ψ) — (Bφ, φ)|, the error between the expectation value of a self-adjoint operator B on an eigenfunction Ψ of a self-adjoint Hamiltonian H and the value given by an approximating vector φ, is obtained when H is a radial Schödinger operator and B is multiplicative and unbounded. The analysis makes use of point and asymptotic estimates for Ψ.