Identification of Geometric Potential from Quantum Conditions for a Particle on a Curved Surface

TL;DR

This paper derives the geometric potential for a particle constrained on a curved surface using a novel approach to quantum conditions and quantization, enhancing understanding of quantum behavior in curved geometries.

Contribution

It introduces a new method for constructing quantum conditions and quantization that yields the geometric potential via thin-layer quantization.

Findings

Derived the geometric potential from quantum conditions

Unified position, momentum, and Hamiltonian quantization

Provided a consistent framework for particles on curved surfaces

Abstract

Combination of a construction of unambiguous quantum conditions out of the conventional one and a simultaneous quantization of the positions, momenta, angular momenta and Hamiltonian leads to the geometric potential given by the so-called thin-lay quantization.