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Complementarity and Classical Limit of Quantum Mechanics: Energy Measurement aspects

In the present contribution we discuss the role of experimental limitations in the classical limit problem. We studied some simple models and found that Quantum Mechanics does not re-produce classical mechanical predictions, unless we consider the experimental limitations ruled by uncertainty principle. We have shown that the discrete nature of energy levels of integrable systems can be accessed by classical measurements. We have defined a precise limit for this procedure. It may be used as a tool to define the classical limit as far as the discrete spectra of integrable systems are concerned. If a diffusive environment is considered, we conclude that the "lifetime" of discreteness is approximately $1/κ$ ($κ$ is the diffusion constant), thus it was possible to relate the classical limit of a spectra with the action of an environment and experimental resolution.