Consider a quantum particle inside a 3D potential box. One can compute the pressure that it exerts on the walls, it's OK.
But what puzzles me is how do we actually measure such a pressure? If we take any macroscopic system with a single particle inside, the pressure will be negligible. Taking many particles forming a gas would make this too far from the ground state, so it's not really quantum (in the quantum regime this would no longer be a gas). Taking something like a semiconductor quantum dot seems to make pressure measurement unrealizable, because the dot walls are very strong, and there's much more deformation because of lattice constant mismatch than because of electron pressure on the walls.
So, what would be a realizable experiment to measure the pressure of a quantum particle, confined in the box, on the box walls?