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

We investigate the quantized magnetic fluxes through the excited state orbits corresponding to the vertical bar n, l, m(j)> states of the hydrogen atom in the absence of an external magnetic field. The sources of the magnetic fields are taken to be that of the proton magnetic moment mu(p), and the electron magnetic moment mu(e) (or mu(j)), which has two components, namely, the orbital part mu(1) and the spinning part We show that the quantized magnetic fluxes through these orbits take the form Phi(n, l, m(j)) =[n - l - m(j)] Phi(0) = [n - l - m(s)]Phi(0) where Phi(0) = hc/e is the flux quanta. The present result gives 0 access to the spin flip-floppings in the optical transitions of the hydrogen atom. It is also believed to be of significant help in understanding the recent observations of spin relaxation in excitonic transitions (such as 1s -> 2p or 2p -> 3d) in nanostructures.