The relation established by the virial theorem is well pronounced in the case of potential energies that are power law functions of distance. In quantum mechanics, a similar analog is present, although it's not for the time average but rather is for the expectation value. Like for a hydrogen like atom (reference: Quantum Mechanical Problems,Constantinescu and Magyari problem 3/8).
My question is how do we examine the case of a dielectronic helium atom, where electric interactions are mediated by $n = −1$ powerlaw functions between each pair of particles. Would the virial theorem hold? What would be the effects of the interchange interaction of quantum mechanics?
Note: Power law functions as mentioned in Landau and Lifshitz Vol.I