Quantum hard spheres in a channel

A quantum hard-sphere system bounded by two parallel rigid walls is studied at absolute zero by numerically integrating the Schr\"odinger equation for the system. A very pronounced layered structure in the density profile across the channel is observed. The numerical calculations are performed on fairly small systems of about 64 hard spheres. It is also found that the layered structure is very sensitive to the distance between the walls. A comparison is made with the results of variational calculations which also show definite but less striking layered structures. A classical hard-sphere fluid in a similar geometry again shows a layered structure which is also sensitive to the distance between the walls. We suggest that the occurrence of the layers can be semiquantitatively related to the oscillations exhibited by the radial distribution function at the same density.