Theta-Quantization of the Orbital Angular Momentum Operator by means of Noncommutative Geometry

TL;DR

This paper explores theta-quantization of the orbital angular momentum operator on a noncommutative lattice, showing its eigenfunctions and eigenvalues are equivalent to those in standard quantum mechanics, thus bridging noncommutative geometry and quantum theory.

Contribution

It introduces a theta-quantization framework for orbital angular momentum on noncommutative lattices, establishing their spectral equivalence to conventional quantum mechanics.

Findings

Eigenfunctions and eigenvalues are constructed for the noncommutative lattice case.

Spectral equivalence with conventional quantum mechanics is demonstrated.

Provides a geometric interpretation linking noncommutative geometry to quantum operators.

Abstract

The eigenfunctions and eigenvalues of orbital angular momentum operator on noncommutative lattice for a circle poset by theta-quantization are constructed, and it is demonstrated that they are equivalent to those of the conventional quantum mechanics.