Coulomb oscillations as a remedy for the helium atom

Abstract

The largest failure of the old, Bohr-Sommerfeld quantum theory was with the helium atom. It brought about the theory's demise. I show that this failure does not originate, as commonly believed, with the orbit concept per se. Instead, it was caused by the wrong choice of orbits, compounded by ignorance of the exclusion principle. Choosing semiclassical electron oscillations through the He nucleus, I calculate a singlet ground-state energy that rivals in accuracy with quantum-mechanical results. The same method reveals Bohr's historic energy value as the forbidden triplet ground state--a result beyond the reach of quantum mechanics. At the qualitative level, the concept of Coulomb oscillations visually explains the major features in the He double spectrum in terms of crossed or parallel orbit orientation.