Abstract
The generalization of the virial theorem is discussed. The case where the potential energy is a sum of homogeneous functions of various degree is investigated. If the potential energy U is composed of a gravitational (or Coulomb) energy and an energy of the short-range repulsion of particles, then virial inequalities of the form 2¯K + Ū < 0 are valid, where K is the kinetic energy. For classical systems of this type, but with a Hamiltonian relativistic in the momenta, the inequality 3Nθ < ¦Ū¦ holds, where N is the number of particles in the system, θ = kT, T is the temperature, and k is Boltzmann's constant.
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Ya. P. Terletskii, Statistical Physics [in Russian], Vysshaya Shkola, Moscow (1973), pp. 87–90.
A. S. Davydov, Quantum Mechanics, Pergamon (1965).
S. Chandrasekhar, Introduction to the Study of Stellar Structure, Dover, New York (1958).
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Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 76–79, June, 1979.
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Terletskii, Y.P. Quantum and relativistic virial inequalities. Soviet Physics Journal 22, 632–635 (1979). https://doi.org/10.1007/BF00891557
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DOI: https://doi.org/10.1007/BF00891557