Quantizing preserving Noether symmetries

2011/08/10 by M. C. Nucci, Nucci, M. C.
Chemistry · Mathematics · Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #Molecular spectroscopy and chirality #Nonlinear Waves and Solitons #Quantum Mechanics and Non-Hermitian Physics #Quantum Physics (quant-ph) #math-ph #math.MP #quant-ph

paper · pdf · doi:10.48550/arxiv.1108.2300

arxiv created 2011/08/10 · openalex publication_date 2011/08/10 · arxiv updated 2011/08/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A procedure which obviates the constraint imposed by the conflict between consistent quantization and the invariance of the Hamiltonian description under nonlinear canonical transformation is proposed. This new quantization scheme preserves the Noether point symmetries of the underlying Lagrangian in order to construct the Schrödinger's equation. As an example, the quantization of the `goldfish' many-body problem extensively studied by Calogero et al. is presented.

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