Quantization of the dynamics of a particle on a double cone by preserving Noether symmetries

TL;DR

This paper develops a quantization method for a particle on a double cone that preserves Noether symmetries, leading to different quantum descriptions than previous approaches, and compares these results.

Contribution

It introduces a symmetry-preserving quantization scheme for particles on a double cone, contrasting with earlier methods and highlighting the importance of Noether symmetries.

Findings

Different quantum equations obtained compared to previous methods

Preservation of Noether symmetries influences the quantization outcome

Comparison shows the impact of symmetry preservation on quantum models

Abstract

The classical quantization of the motion of a free particle and that of an harmonic oscillator on a double cone are achieved by a quantization scheme [M.C. Nucci, Theor. Math. Phys. 168 (2011) 994], that preserves the Noether point symmetries of the underlying Lagrangian in order to construct the Schroedinger equation. The result is different from that given in [K. Kowalski, J.Rembielnski, Ann. Phys. 329 (2013) 146]. A comparison of the different outcomes is provided.