Topological quantization of the harmonic oscillator

TL;DR

This paper introduces a novel topological quantization method to derive the harmonic oscillator's energy spectrum, linking classical mechanics and topological invariants through fiber bundle theory.

Contribution

It presents a new approach to quantization using topological invariants of fiber bundles within Maupertuis' classical mechanics framework.

Findings

Energy spectrum derived from topological invariants

Establishes a connection between classical configurations and quantum spectra

Demonstrates the applicability of topological methods to quantum systems

Abstract

We present a derivation of the energy spectrum of the harmonic oscillator by using the alternative approach of topological quantization. The spectrum is derived from the topological invariants of a particular principal fiber bundle which can be assigned to any configuration of classical mechanics, when formulated according to Maupertuis formalism.