Abstract
For a particle in a box, the operator - i ∂_x is not Hermitean. We provide an alternative construction of a momentum operator p = p_R + i p_I, which has a Hermitean component p_R that can be extended to a self-adjoint operator, as well as an anti-Hermitean component i p_I. This leads to a description of momentum measurements performed on a particle that is strictly limited to the interior of a box.