Independent particle Schrödinger fluid: Moments of inertia

The philosophy of the single particle Schrödinger fluid, especially as regards the velocity fields which find such a natural role therein, is applied to the study of the moments of inertia of independent fermion system. It is shown that three simplified systems exhibit the rigid-body rotational velocity field in the limit of large A, and that the leading deviations, both on the average and fluctuating, from this large-A limit can be described analytically, and verified numerically. For a single particle in a Hill-Wheeler box the moments are studied numerically, and their large fluctuations identified with the specific energy level degeneracies of its parallelepiped shape. The full assemblage of these new and old results is addressed to the question of the necessary and sufficient condition that the moment has the rigid value. Counter examples are utilized to reject some conditions, and the conjecture is argued that unconstrained shape equilibrium might be the necessary and sufficient condition. The spheroidal square-well problem is identified as a promising test case.