An elementary derivation of the quantum virial theorem from Hellmann-Feynman theorem

A simple proof of the quantum virial theorem that can be used in undergraduate courses is given. The proof proceeds by first showing that the energy eigenvalues of a Hamiltonian remain invariant under a scale transformation. Then invoking the Hellmann-Feynman theorem produces the final statement of...

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Bibliographic Details
Published in:European journal of physics 2016-07, Vol.37 (4), p.45405
Main Authors: peko lu, Y, Turgut, S
Format: Article
Language:English
Subjects:
Hellmann-Feynman theorem
quantum virial theorem
scale transformation
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Summary:A simple proof of the quantum virial theorem that can be used in undergraduate courses is given. The proof proceeds by first showing that the energy eigenvalues of a Hamiltonian remain invariant under a scale transformation. Then invoking the Hellmann-Feynman theorem produces the final statement of the virial theorem.
ISSN:0143-0807
1361-6404
DOI:10.1088/0143-0807/37/4/045405