Remarks on geometric quantum mechanics. (English) Zbl 1078.81029
Summary: Pursuing the aims of geometric quantum mechanics, it is shown in a geometrical fashion that, at least in finite dimension, Schrödinger dynamics enjoys classical complete integrability, and several consequences therefrom are deduced, including a Hannay-type reinterpretation of Berry’s phase and a geometric description of some aspects of the quantum measurement problem.
MSC:
| 81Q70 | Differential geometric methods, including holonomy, Berry and Hannay phases, Aharonov-Bohm effect, etc. in quantum theory |
| 37J35 | Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests |
| 37N20 | Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics) |
| 58J90 | Applications of PDEs on manifolds |
| 81P15 | Quantum measurement theory, state operations, state preparations |
Keywords:
Geometric quantum mechanics; Complete integrability; Geometric phases; Quantum measurement theoryReferences:
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