To what extent are canonical and coherent state quantizations physically equivalent?

TL;DR

This paper examines whether coherent state quantization aligns with canonical quantization in predicting physical observations, especially in non-relativistic quantum systems, and validates CS quantization using vibrational spectroscopy data.

Contribution

It demonstrates that coherent state quantization is a valid alternative to canonical quantization for standard dynamical observables and tests its validity with experimental vibrational spectroscopy data.

Findings

CS quantization matches canonical predictions for position, momentum, and energy.

CS quantization can be distinguished from canonical quantization based on physical data.

Vibrational spectroscopy data supports the validity of CS quantization.

Abstract

We investigate the consistency of coherent state (or Berezin-Klauder-Toeplitz, or anti-Wick) quantization in regard to physical observations in the non- relativistic (or Galilean) regime. We compare this procedure with the canonical quantization (on both mathematical and physical levels) and examine whether they are or not equivalent in their predictions: is it possible to dif- ferentiate them on a strictly physical level? As far as only usual dynamical observables (position, momentum, energy, ...) are concerned, the quantization through coherent states is proved to be a perfectly valid alternative. We successfully put to the test the validity of CS quantization in the case of data obtained from vibrational spectroscopy (data that allowed to validate canonical quantization in the early period of Quantum Mechanics).