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 $${\mathcal{G}}_{op}=\frac{e}{\hslash }(\vec{\sigma }\cdot \vec{A})$$ 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 $$\frac{eg}{c}=(n_1-n_2)\alpha$$ 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.