Similarity of Wigner's delay time to the virial theorem for scattering by a central field

Abstract

The quantum-mechanical virial theorem for scattering of a particle by a central force is expressed in terms of Wigner's definition of time delay, tau = 2h deta/dE. By using semiclassical approximations, the quantum-mechanical virial is transformed into the classical virial and tau becomes exactly the classical delay time.