Quantum mechanical virial theorem in systems with translational and rotational symmetry - Quantum PhysicsReport as inadecuate




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Abstract: Generalized virial theorem for quantum mechanical nonrelativistic andrelativistic systems with translational and rotational symmetry is derived inthe form of the commutator between the generator of dilations G and theHamiltonian H. If the conditions of translational and rotational symmetrytogether with the additional conditions of the theorem are satisfied, thematrix elements of the commutator G, H are equal to zero on the subspace ofthe Hilbert space. Normalized simultaneous eigenvectors of the particular setof commuting operators which contains H, J^{2}, J {z} and additional operatorsform an orthonormal basis in this subspace. It is expected that the theorem isrelevant for a large number of quantum mechanical N-particle systems withtranslational and rotational symmetry.



Author: Domagoj Kuic

Source: https://arxiv.org/







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