old quantum theory

The old quantum theory is the loose collection of ideas and rules that physicists used between roughly 1900 and 1925, after Planck's quantum was born but before the full machinery of quantum mechanics existed. It was not a single coherent theory so much as a patchwork: classical mechanics with extra quantization conditions grafted on by hand to force certain quantities, like energy or angular momentum, to take only discrete values.

Its great monuments are Planck's blackbody law, Einstein's photons, the Bohr model of hydrogen, and the Bohr–Sommerfeld rules that extended quantization to more general orbits. These successes were real and important, and for a time they made remarkable predictions. But the approach worked by intuition and analogy, choosing which quantities to quantize on a case-by-case basis rather than from any deep underlying principle.

Its cracks showed plainly with multi-electron atoms, the intensities of spectral lines, and the helium atom, which it simply could not solve. The old quantum theory was a brilliant scaffolding, indispensable for building the real edifice but destined to be taken down once it was up. The genuine theory arrived in 1925–1926 with Heisenberg's matrix mechanics and Schrödinger's wave mechanics, which derived the quantization the old theory had merely imposed.