Magnetic Charge of the Stark States of Hydrogen Atoms

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.