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Il Nuovo cimento della Società italiana di fisica. B/Il Nuovo cimento B

Hamiltonian vector fields in quantum mechanics

Renzo Cirelli, P. Lanzavecchia

Published Feb 1, 1984• 45 citations
Publisher
DOI
10.1007/bf02748976

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Based on classical mechanical picture of physical objects, quantum-mechanical measurements are formulated and analyzed in an abstract way. We interpret a dynamical flow generated by a Hamiltonian vector field as a description of the effect on the objects caused by a device or an environment. By expressing contexts of measurement explicitly, a matrix representation of observables on a finite dimensional Hilbert space is constructed. A quantum-mechanical state vector is introduced as something on which a dynamical flow generated by a Hamiltonian vector field acts. We find conditions that enable us to obtain the Dirac's quantization rule for the mean values. At the same time, several characteristics (i.e., rectifiability, a generator of symmetry, an invariant mean) of quantum-mechanical measurements are formulated in our formalism.