The Quantum Trihedron

TL;DR

This paper investigates the quantum properties of a geometric shape called the trihedron, demonstrating that Bohr-Sommerfeld quantization of its area yields an evenly spaced energy spectrum.

Contribution

It provides a novel application of Bohr-Sommerfeld quantization to the trihedron, linking geometric area quantization to spectral properties.

Findings

Quantization reproduces an equidistant spectrum

Exact match with previously known spectral results

Establishes a geometric basis for quantum spectra

Abstract

The convex hull on three points in two dimensional euclidean space of three flat edges (trihedron) was studied. The Bohr-Sommerfeld quantization of the area of space is performed. It is shown that it reproduces exactly the equidistant spacing spectrum found elsewhere.