Magnetic Charge of the Stark States of Hydrogen Atoms

TL;DR

This paper proposes that Stark states of hydrogen atoms may possess a quantized magnetic charge related to their quantum numbers, suggesting a novel magnetic property of atomic states with potential experimental verification.

Contribution

It introduces a conjecture that hydrogen Stark states have a quantized magnetic charge linked to quantum numbers, supported by a derived expectation value and quantization formula.

Findings

Expectation value of magnetic charge operator derived as g = e(n_1 - n_2)

Magnetic charge obeys a Dirac-Saha type quantization formula involving the fine structure constant

An experimental setup is proposed to test the magnetic charge conjecture

Abstract

It is conjectured that Stark states of excited hydrogen atom posses magnetic charge for which the quantum mechanical operator is $${\cal G}_{op} = {e\over \hbar} (\vec\sigma\cdot\vec A)$$ where $\vec A$ is the Runge-Lenz vector. The expectation value $g$ of this operator for Stark states is found to be $$ g = e(n_1-n_2)$$ which obeys a Dirac-Saha type quantization formula $${eg\over c} = (n_1-n_2)\alpha$$ where $\alpha$ is the fine structure constant and $n_1$ and $n_2$ are parabolic quantum numbers. An experimental arrangement is outlined to test this conjecture.