Effective quantum number for axially symmetric problems

TL;DR

This paper extends the concept of an effective quantum number to axially symmetric potentials, providing a semiclassical quantization condition applicable to these more general systems.

Contribution

It introduces a generalized effective quantum number for axially symmetric problems, expanding the applicability of previous models to a broader class of potentials.

Findings

Provides a new semiclassical quantization condition for axially symmetric potentials.

Generalizes the effective quantum number concept beyond central symmetry.

Enhances theoretical tools for quantum systems with axial symmetry.

Abstract

We generalize the universal effective quantum number introduced earlier for centrally symmetric problems. The proposed number determines the semiclassical quantization condition for axially symmetric potentials.