Rise and fall of the old quantum theory
| dc.creator | Bucher, Manfred | |
| dc.date | 2008-02-11 | |
| dc.date.accessioned | 2026-07-07T09:19:50Z | |
| dc.date.available | 2026-07-07T09:19:50Z | |
| dc.description | 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. | |
| dc.description | 34 pages, 12 figures | |
| dc.identifier | https://arxiv.org/abs/0802.1366 | |
| dc.identifier | http://arxiv.org/abs/0802.1366 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/154542 | |
| dc.subject | History and Philosophy of Physics | |
| dc.subject | Physics Education | |
| dc.title | Rise and fall of the old quantum theory | |
| dc.type | text |