A simple formula is presented for the change in energy of a quantum system in a box when the box is infinitesimally deformed. The result is applied to rederive a formula given by Bartonetal., [Am. J. Phys.58, 751–755 (1990)] for the difference in energy of a bound state calculated with and without box boundary conditions. The formula can also be used to discuss pressure in a quantum system. A generalization of the result has been used for calculating scattering amplitudes for waves scattered by a rough extended surface. Here, a similar manifestly reciprocal result is derived for scattering by bounded objects.