Universal Effective Quantum Number for Centrally Symmetric Problems

TL;DR

This paper introduces a universal effective quantum number that accurately predicts energy level orderings in centrally symmetric potentials across different dimensions, aiding the construction of atomic shell systems.

Contribution

It presents a novel universal quantum number applicable to any space dimensionality, improving the understanding of energy levels in symmetric potentials.

Findings

High accuracy in level ordering predictions

Agreement with known exact results

Application to atomic electron shell systems

Abstract

An effective quantum number determining with high accuracy the levels ordering in arbitrary centrally symmetric potentials for any space dimensionality is introduced and calculated by means of certain universal methods based on the known estimates for the total number of the bound states in the same potential for various dimensionality. Coincidence with some known exact results is demonstrated. The effective number is used for constructing the periodical system of the atomic electron shells.