On the definition of Quantum Free Particle on Curved Manifolds
C. Destri, P. Maraner, E. Onofri
TL;DR
This paper proposes a natural, self-consistent way to define a quantum free particle on curved manifolds by focusing on dynamics restricted to co-dimension one submanifolds.
Contribution
It introduces a novel approach to defining quantum free particles on curved spaces through submanifold restriction, addressing a gap in existing formulations.
Findings
Provides a consistent mathematical framework for quantum particles on curved manifolds
Demonstrates the approach's applicability to various curved geometries
Lays groundwork for future quantum mechanics on complex manifolds
Abstract
A selfconsistent definition of quantum free particle on a generic curved manifold emerges naturally by restricting the dynamics to submanifolds of co-dimension one. PACS 0365 0240
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