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Abstract: The old quantum theory of Bohr and Sommerfeld was abandonned for the wrongreason. Its contradictions were caused not by the orbit concept but by a mentalbarrier-the inconceivability that an electron might collide with the atomicnucleus. Removing that barrier resolves the theory-s main failures-incorrectorbital momenta, He atom, H2+ molecule ion. The inclusion of electronoscillations through the nucleus-a concept called -Coulomboscillator-renders the old quantum theory consistent with quantum mechanicsalthough devoid of wave character. The triple success of the Bohr-Sommerfeldmodel is its correct description of the H atom and one-electron ionsconcerning 1 the energy levels Enl, 2 the orbital angular momenta Lnl-ifcorrected as Lnl^2 = ll+1 hbar^2 and with the Coulomb oscillatorincluded-and 3 the orbits- space quantization-with Lnlz = ml hbar. Theseachievements are succinctly represented by the principal, angular and magneticquantum numbers n, l, ml and visualized by orbital ellipse geometry-majoraxis, vertex curvature, and tilt angle, respectively. Orbit geometry alsoaccounts for the average orbit size. Moreover, the Coulomb oscillator providesa natural explanation of isotropic hyperfine interaction. The shortcomings ofthe old quantum theory lie in its neglect of three properties ofparticles-their spin, their wave nature and their quantum statistics. Thesedeficiencies notwithstanding, the visual appeal of the Bohr-Sommerfeld modelremains a pedagogical asset to complement the abstract character of quantummechanics.

Autor: Manfred Bucher

Fuente: https://arxiv.org/

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