Time-dependent differential virial theorems

In this article we derive for an arbitrary, real, local (multiplicative), t ime-dependent (TD) external potential, the differential form of the virial theorem for the pure state in TD Schrodinger theory. We contrast this pure- state theorem with the many-body theory equation of motion for both equilib rium and nonequilibrium phenomena. We also derive the corresponding pure-st ate theorem for a model system of noninteracting fermions with equivalent T D density. These theorems are valid for both adiabatic and sudden switching on of the external potential. The theorems furthermore lead to a line-inte gral expression for the local effective potential of the noninteracting sys tem that may be provided the physical interpretation, at each instant of ti me, as being the work done to move an electron in the force of a conservati ve field. (C) 2000 John Wiley & Sons, Inc.