Nonrelativistic Quantum Particle in a Curved Space as a Constrained System

TL;DR

This paper investigates the quantum dynamics of a nonrelativistic particle constrained in a curved space, focusing on defining a clear quantum Hamiltonian through operator and functional approaches.

Contribution

It provides a systematic analysis of the quantum Hamiltonian formulation for particles in curved spaces using operator and functional methods.

Findings

Derived unambiguous quantum Hamiltonian for constrained particles in curved space.

Clarified the relationship between operator and functional formulations.

Enhanced understanding of quantum dynamics in curved geometries.

Abstract

The operator and the functional formulations of the dynamics of constrained systems are explored for determining unambiguously the quantum Hamiltonian of a nonrelativistic particle in a curved space.