Virial Theorem for Angular Displacement and Torque

The usual Virial theorem is expressed through the coordinate and the force, 2áT? = áXfracdVdX? = -áXF?2langle Trangle =langle Xfrac{dV}{dX}rangle =-langle XFrangle , F=-fracdVdXF=-frac{dV}{dX}, XF is the work done by the force F, T is the kinetic energy. In this paper we extend the usual discussion on the Virial theorem about coordinate-force variables to the case of angular displacement-torque variables. By virtue of introducing the entangled state representation and the bosonic operator realization of the Hamiltonian of quantum pendulum system we derive the Virial theorem for angular variable and torque.