Quantized magnetic flux through the ground-state orbit of the hydrogen atom

We have investigated the spin-dependent quantized magnetic fluxes through the ground-state electronic orbit of the hydrogen atom. We show that the corresponding fluxes are (1/2)Φ₀ for the spin-up case and (3/2)Φ ₀ for the spin-down case, respectively, where Φ₀ = hc/e is the flux quantum. Using the energy-flux proportionality, we also show that the spin-up case (where the electron spin is antiparallel to the proton spin, resulting in zero total spin) is the spin-dependent ground state of the hydrogen atom. The present result helps to understand the spin flip-flop in excitonic transitions in nanostructures.