HARMONIC-POTENTIAL THEOREM - IMPLICATIONS FOR APPROXIMATE MANY-BODY THEORIES

We consider interacting particles in an external harmonic potential. W e extend the B = 0 case of the generalized Kohn theorem, giving a ''ha rmonic-potential theorem'' (HPT), demonstrating rigid, arbitrary-ampli tude, time-oscillatory Schrodinger transport of a many-body eigenfunct ion. We show analytically that the time-dependent local-density approx imation (TDLDA) satisfies the HPT exactly. Other approximations, such as linearized TDLDA with frequency-dependent exchange correlation kern el and certain inhomogeneous hydrodynamic formalisms, do not. A simple modification permits such explicitly frequency-dependent local theori es to satisfy the HPT, however.