Time-dependent differential virial theorems

✍ Scribed by Zhixin Qian; Viraht Sahni

• Publisher: John Wiley and Sons
• Year: 2000
• Tongue: English
• Weight: 200 KB
• Volume: 78
• Category: Article
• ISSN: 0020-7608
• DOI: 10.1002/(sici)1097-461x(2000)78:5<341::aid-qua5>3.0.co;2-r

✦ Synopsis

In this article we derive for an arbitrary, real, local (multiplicative), time-dependent (TD) external potential, the differential form of the virial theorem for the pure state in TD Schrödinger theory. We contrast this pure-state theorem with the many-body theory equation of motion for both equilibrium and nonequilibrium phenomena. We also derive the corresponding pure-state theorem for a model system of noninteracting fermions with equivalent TD density. These theorems are valid for both adiabatic and sudden switching on of the external potential. The theorems furthermore lead to a line-integral expression for the local effective potential of the noninteracting system that may be provided the physical interpretation, at each instant of time, as being the work done to move an electron in the force of a conservative field.