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We use the functorial properties of Rieffel's pseudodifferential calculus tostudy families of operators associated to topological dynamical systems actedby a symplectic space. Information about the spectra and the essential spectraare extracted from the quasi-orbit structure of the dynamical system. Thesemi-classical behavior of the families of spectra is also studied.

Rieffel's pseudodifferential calculus and spectral analysis of quantum Hamiltonians