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On the virial theorem in quantum mechanics

Herbert Leinfelder

Integral Equations and Operator TheoryJun 1, 19815 citations

Simple derivation of the quantum mechanical virial theorem

T. C. Ernest

American Journal of PhysicsMay 1, 19911 citation

Canonical formulation of the scale transformation and virial theorem for quantum systems

Ken-ichi Takiuchi, Tadashi Toyoda

AIP conference proceedingsJan 1, 19990 citations

Virial theorem and generalized momentum in quaternionic quantum mechanics

Sergio Giardino

arXiv:1911.06831The European Physical Journal PlusJan 1, 202030 citations

A note on potentials with non-trivial scales and the quantum-mechanical virial theorem

E. A. Castro

Il Nuovo cimento della Società italiana di fisica. B/Il Nuovo cimento BSep 1, 19960 citations

Simple Generalization of the Quantum Mechanical Virial Theorem for Nonrelativistic Systems with Rotational Symmetry

Domagoj Kuić

In this paper we show that the generalization of the virial theorem can be achieved for nonrelativistic quantum mechanical systems under the conditions of rotational symmetry and the constancy of the trace of moment of inertia tensor. Under these conditions the matrix elements of the commutator of the generator of dilations G and the Hamiltonian H are equal to zero on the subspace of the Hilbert space generated by the simultaneous eigenvectors of the particular maximal set of commuting self-adjoint operators which contains H, J2, Jz, the trace of the moment of inertia tensor TrI and additional operators. The result obtained is relevant for an important class of N-particle nonrelativistic quantum mechanical systems.In this paper we show that the generalization of the virial theorem can be achieved for nonrelativistic quantum mechanical systems under the conditions of rotational symmetry and the constancy of the trace of moment of inertia tensor. Under these conditions the matrix elements of the commutator of the generator of dilations G and the Hamiltonian H are equal to zero on the subspace of the Hilbert space generated by the simultaneous eigenvectors of the particular maximal set of commuting self-adjoint operators which contains H, J2, Jz, the trace of the moment of inertia tensor TrI and additional operators. The result obtained is relevant for an important class of N-particle nonrelativistic quantum mechanical systems.

Physical Science International JournalJan 10, 20160 citations

Quantum Mechanical Virial Theorem in Systems with Translational and Rotational Symmetry

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