  We study the equilibrium thermodynamics of quantum hard spheres in the
infinite-dimensional limit, determining the boundary between liquid and glass
phases in the temperature-density plane by means of the Franz-Parisi potential.
We find that as the temperature decreases from high values, the effective
radius of the spheres is enhanced by a multiple of the thermal de Broglie
wavelength, thus increasing the effective filling fraction and decreasing the
critical density for the glass phase. Numerical calculations show that the
critical density continues to decrease monotonically as the temperature
decreases further, suggesting that the system will form a glass at sufficiently
low temperatures for any density.
