In recent years, it has been recognized that treatment of the spectral problem should be associated
with closed orbits. This paper proves that the closed orbit obtained by Bohr using numerical algebraic
equation is reasonable both mathematically and physically and that the de Broglie wavelength of the
electron in the hydrogen atom is equal to the circumference of its orbit. By Bohr model and de Broglie’s
matter-wave thought, some quantization conditions, electronic transition formulae, a mechanism and
details of emitting photon wave train, a filling order of electrons in the periodic table, and Madelung
rule have been deduced theoretically. We solve the Löwdin’s challenge problem.
