Schrödinger’s Breakthrough

Jim Baggott, John L. Heilbron

Abstract In June 1925 Heisenberg made the breakthrough that would lead to matrix mechanics. The theory was abstract, offered no means for visualizing the mechanics of the atom, and its application required a lot of heavy lifting. Erwin Schrödinger subsequently made the breakthrough that would lead to wave mechanics, building on Louis de Broglie’s association of a wave with an electron. In Schrödinger’s wave equation the quantum numbers of the hydrogen atom arise naturally. He argued that his ‘wavefunction’ offered a realistic description of the electron in an atom, and sought to eliminate Bohr’s discontinuous quantum jumps. But in the spring of 1926, Max Born offered an enduring alternative. The modulus-square of the wavefunction is a measure of probability in an unvisualizable microphysics. In an intense debate with Bohr, Schrödinger demanded a theory based on logical concepts free from contradictions. Bohr was left to ponder what this might mean.

S. Brandt

Abstract The breakthrough to quantum mechanics was, as we have seen in Episode 37, achieved by Heisenberg in the summer of 1925 and the theory, in the form now known as matrix mechanics, was completed a little later by Born, Heisenberg, and Jordan. From his first days as a student Heisenberg had belonged to groups which worked on quantum theory. He was, so to speak, totally immersed in the field and reached his solution at the age of twenty-three. At the turn of the year 1925/26 quantum mechanics was created again, now clad as wave mechanics [1], by Schrödinger, who did not belong to an active research group in the field and who was then thirty-eight. As soon as it appeared wave mechanics was popular with physicists, because it was based on familiar differential equations and not on matrix formalism which was practically unknown.

Luca Viganò, Diego Sempreboni

J. L. Heilbron

‘Enthusiastic resignation’ describes Bohr’s work with Wolfgang Pauli and Werner Heisenberg. ‘Resignation’ refers to their realization that the electron orbits that had served as the basis of Bohr’s theory had only ‘symbolic’ value. They took the correspondence principle as a guide to translating symbols describing the orbits, like position and momentum, into symbols specifying the values of observable products of atoms, like the frequency and intensity of spectral lines. Heisenberg’s breakthrough in the summer of 1925, based on a particulate view of matter, provided a basis for a coherent description of the phenomena to which atomic electrons give rise. Almost simultaneously, Erwin Schrödinger found another route to the same mathematical solution, based on a wave picture of matter, which avoided discontinuity and made calculations easier. In answering Schrödinger’s challenge, Heisenberg invented the Uncertainty Principle and Bohr worked out a more general reconciliation of the quantum puzzles, which he called ‘complementarity’.

Nishikawa Taisho