Truncated space calculations of "exact" bound-state energies

A method is developed for correcting truncated harmonic oscillator basis calculations of one-body bound-state energies for the omitted matrix elements of the kinetic energy operator. The method is only applicable when the potential energy operator is accurately represented in the truncated space. As an example of the method, the Hartree-Fock potential for the oxygen nucleus is considered with the Tabakin nucleon-nucleon potential. In a very large space this potential has only one bound $s$ state, though solving the Schrödinger equation in coordinate space yields two. The method gives this second bound state's energy quite accurately.