Abstract
In ordinary quantum mechanics for finite systems, the time evolution induced by Hamiltonians of the form\(H = \frac{{P^2 }}{{2m}} + V(Q)\) is studied from the point of view of *-automorphisms of the CCRC*-algebra\(\bar \Delta \) (see Ref. [1, 2]). It is proved that those Hamiltonians do not induce *-automorphisms of this algebra in the cases: a)\(V \in \bar \Delta \) and b)V εL ∞ (ℝ,dx) ∩L 1 (ℝ,dx), except when the potential is trivial.
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Communicated by W. Hunziker
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Fannes, M., Verbeure, A. On the time evolution automorphisms of the CCR-algebra for quantum mechanics. Commun.Math. Phys. 35, 257–264 (1974). https://doi.org/10.1007/BF01646197
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DOI: https://doi.org/10.1007/BF01646197