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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

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    $\begingroup$ 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 $\endgroup$ – user108787 Nov 7 '16 at 17:13
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    $\begingroup$ @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 $\endgroup$ – Naveen Balaji Nov 7 '16 at 17:19

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