Revised Virial Theorem for Hamiltonians with Coordinates-Momentum Coupling Terms

Abstract

Usually the Virial theorem, which can be derived from the Feynman–Hellmann theorem, applies to Hamiltonians without coordinates-momentum coupling. In this paper we discuss when there are such kind of couplings in Hamiltonians then how the Virial theorem should be modified. We also discuss the energy contribution arising from the coordinates-momentum coupling for a definite energy level.