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arXiv · 1110.6678

Quantization with Action-Angle Coherent States

J. -P. Gazeau·R. Kanamoto
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Abstract

For a single degree of freedom confined mechanical system with given energy, we know that the motion is always periodic and action-angle variables are convenient choice as conjugate phase-space variables. We construct action-angle coherent states in view to provide a quantization scheme that yields precisely a given observed energy spectrum ${E_n}$ for such a system. This construction is based on a Bayesian approach: each family corresponds to a choice of probability distributions such that the classical energy averaged with respect to this probability distribution is precisely $E_n$ up to a constant shift. The formalism is viewed as a natural extension of the Bohr-Sommerfeld rule and an alternative to the canonical quantization. In particular, it also yields a satisfactory angle operator as a bounded self-adjoint operator.

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J. -P. Gazeau, R. Kanamoto. 2011-10-31. Quantization with Action-Angle Coherent States. https://doi.org/10.1088/1742-6596%2F343%2F1%2F012038

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