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

İPEKOĞLU Y., TURGUT S.

EUROPEAN JOURNAL OF PHYSICS, vol.37, no.4, 2016 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 37 Issue: 4
  • Publication Date: 2016
  • Doi Number: 10.1088/0143-0807/37/4/045405
  • Journal Name: EUROPEAN JOURNAL OF PHYSICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Keywords: quantum virial theorem, Hellmann-Feynman theorem, scale transformation, FORCES
  • Middle East Technical University Affiliated: Yes

Abstract

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.