  Based on the recent construction of a self-adjoint momentum operator for a
particle confined in a one-dimensional interval, we extend the construction to
arbitrarily shaped regions in any number of dimensions. Different components of
the momentum vector do not commute with each other unless very special
conditions are met. As such, momentum measurements should be considered one
direction at a time. We also extend other results, such as the Ehrenfest
theorem and the interpretation of the Heisenberg uncertainty relation to higher
dimensions.
