Virial Theorem Generalized

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Abstract
The quantum mechanical virial theorem as usually stated is correct only for a bound state of an unconfined system, because the proof depends on the vanishing not only of ψ but also of δψ/δxα at the bounding surface. The correct form is given and used to deduce the equation of state. A generalized form of the virial theorem is deduced for both quantum and classical mechanics, which may be used to obtain nonhydrostatic equations of state, i.e., expressions for the Cauchy stress tensor.

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