Quantum Mechanical Virial Theorem in Systems with Translational and Rotational Symmetry |
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Authors: | Domagoj Kui? |
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Institution: | 1. Faculty of Science, University of Split, N. Tesle 12, 21000, Split, Croatia
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Abstract: | 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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