# On Virial theorem and its Quantum mechanical analog

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

• Hi, do you mean hydrogen (in your tag) or helium (in your post). Also, what is an interchange interaction, an exchange of particles I guess. Thanks – user108787 Nov 7 '16 at 17:13
• @CountTo10 I have added hydrogen tag because I have initially mentioned about the QM of hydrogen like atoms, can understand the confusion, will edit the question. Thanks. For the latter question you have asked please see this- en.wikipedia.org/wiki/Exchange_interaction , I'll add this edit too – Naveen Balaji Nov 7 '16 at 17:19