As discussed by O'Sullivan recently in this journal, 1 the elliptical-orbit Sommerfeld model provides a pedagogical bridge from the circular-orbit Bohr model of the hydrogen atom to Schrödinger's wave-mechanical theory. Many of the conundrums that historically brought down the old quantum theory have been resolved by inclusion of straight-line electron orbits through the nucleus (“Coulomb oscillator,” =0),2 omission of the circular Bohr orbits (n), and the (+1) correction for the magnitude of angular momentum.3 However, no benefit in the teaching and learning of introductory quantum mechanics—in fact, more confusion will arise—if the Sommerfeld model is not presented accurately. In that spirit this comment corrects some errors in O'Sullivan's paper.

Faulty average: The average rotational kinetic energy of a Kepler orbit, when correctly derived,4 is

Trot=L...
AAPT members receive access to the American Journal of Physics and The Physics Teacher as a member benefit. To learn more about this member benefit and becoming an AAPT member, visit the Joining AAPT page.