
The authors review several versions of the quantum mechanical virial theorem that exist in the literature. By considering an explicits situation, it is shown that the version contained in the book of \textit{H. L. Cycon}, \textit{R. G. Froese}, \textit{W. Kirsch} and \textit{B. Simon} [Schrödinger operators with applications to quantum mechanics and global geometry. Berlin: Springer (1987; Zbl 0619.47005)] is incorrect. In an appendix it is proved a new version of the virial theorem for self-adjoint operators \(A,H\) which only needs the assumption \(e^{isA}{\mathcal D}(|H|^\sigma) \subset{\mathcal D} (|H|^\sigma)\) for some \(\sigma\geq 1/2\) and a certain continuity property of the sesquilinear form associated with the commutator \([A,H]\).
virial theorem, Applications of operator theory in the physical sciences, self-adjoint operators, Scattering theory for PDEs, Selfadjoint operator theory in quantum theory, including spectral analysis
virial theorem, Applications of operator theory in the physical sciences, self-adjoint operators, Scattering theory for PDEs, Selfadjoint operator theory in quantum theory, including spectral analysis
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