International Journal of Theoretical Physics

, Volume 52, Issue 4, pp 1221–1239 | Cite as

Quantum Mechanical Virial Theorem in Systems with Translational and Rotational Symmetry

  • Domagoj Kuić


Generalized virial theorem for quantum mechanical nonrelativistic and relativistic systems with translational and rotational symmetry is derived in the form of the commutator between the generator of dilations G and the Hamiltonian H. If the conditions of translational and rotational symmetry together with the additional conditions of the theorem are satisfied, the matrix elements of the commutator [G,H] are equal to zero on the subspace of the Hilbert space. Normalized simultaneous eigenvectors of the particular set of commuting operators which contains H, J 2, J z and additional operators form an orthonormal basis in this subspace. It is expected that the theorem is relevant for a large number of quantum mechanical N-particle systems with translational and rotational symmetry.


Quantum mechanics Virial theorem Systems with translational and rotational symmetry Dilations 


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© Springer Science+Business Media New York 2012

Authors and Affiliations

  1. 1.Faculty of ScienceUniversity of SplitSplitCroatia

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