Quantum mechanical virial theorem in systems with translational and rotational symmetry

Details Quantum mechanical virial theorem in systems with translational and rotational symmetry Quantum mechanical virial theorem in systems with translational and rotational symmetry

2009-01-08

arxiv.org/abs/0901.1076v5

Physics

Quantum Physics

29 pages; v5: endnotes transferred to footnotes; minor corrections

Scientific paper

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.

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