Toroidal moments of Schr\"odinger eigenstates

TL;DR

This paper develops a quantum model for a particle on a toroidal helix, calculating eigenstates and toroidal moments, revealing how loop eccentricity influences these quantum properties in contrast to classical expectations.

Contribution

It introduces a quantum framework for particles on a toroidal helix, including curvature effects, and analyzes how loop eccentricity affects toroidal moments.

Findings

Toroidal moments depend strongly on loop eccentricity.

Quantum moments differ significantly from classical predictions.

Eigenfunctions are computed using a basis set approach.

Abstract

The Hamiltonian for a particle constrained to motion near a toroidal helix with loops of arbitrary eccentricity is developed. The resulting three dimensional Schr\"odinger equation is reduced to a one dimensional effective equation inclusive of curvature effects. A basis set is employed to find low-lying eigenfunctions of the helix. Toroidal moments corresponding to the individual eigenfunctions are calculated. The dependence of the toroidal moments on the eccentricity of the loops is reported. Unlike the classical case, the moments strongly depend on the details of loop eccentricity.