Quantization with Action-Angle Coherent States

TL;DR

This paper introduces a novel quantization scheme using action-angle coherent states based on a Bayesian approach, providing precise energy spectra and a well-defined angle operator as an alternative to canonical quantization.

Contribution

It develops a Bayesian-based quantization method utilizing action-angle coherent states, extending the Bohr-Sommerfeld rule and offering a new angle operator.

Findings

Accurately reproduces given energy spectra ${E_n}$

Provides a bounded self-adjoint angle operator

Offers an alternative to canonical quantization

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.