  The old quantum theory of Bohr and Sommerfeld was abandonned for the wrong
reason. Its contradictions were caused not by the orbit concept but by a mental
barrier--the inconceivability that an electron might collide with the atomic
nucleus. Removing that barrier resolves the theory's main failures--incorrect
orbital momenta, He atom, H2+ molecule ion. The inclusion of electron
oscillations through the nucleus--a concept called "Coulomb
oscillator"--renders the old quantum theory consistent with quantum mechanics
(although devoid of wave character). The triple success of the Bohr-Sommerfeld
model is its correct description of the H atom (and one-electron ions)
concerning (1) the energy levels Enl, (2) the orbital angular momenta Lnl--if
corrected as Lnl^2 = l(l+1) hbar^2 and with the Coulomb oscillator
included--and (3) the orbits' space quantization--with (Lnl)z = ml hbar. These
achievements are succinctly represented by the principal, angular and magnetic
quantum numbers (n, l, ml) and visualized by orbital ellipse geometry--major
axis, vertex curvature, and tilt angle, respectively. Orbit geometry also
accounts for the average orbit size. Moreover, the Coulomb oscillator provides
a natural explanation of (isotropic) hyperfine interaction. The shortcomings of
the old quantum theory lie in its neglect of three properties of
particles--their spin, their wave nature and their quantum statistics. These
deficiencies notwithstanding, the visual appeal of the Bohr-Sommerfeld model
remains a pedagogical asset to complement the abstract character of quantum
mechanics.
