In the case where the Hilbert space is a space of functions on a bounded domain, these distinctions have to do with a familiar issue in quantum physics: One cannot define an operator—such as the momentum or Hamiltonian operator—on a bounded domain without specifying "boundary conditions". In mathematical terms, choosing the boundary conditions amounts to choosing an appropriate domain for the operator. Consider, for example, the Hilbert space formula_57 (the space of square-integrable functions on the interval [0,1]). Let us define a "momentum" operator "A" on this space by the usual formula, setting Planck's constant equal to 1: