137 - Arthur I. Miller [51]
Then the French physicist Louis de Broglie suggested that electrons might be waves—in other words, that material objects, such as ourselves, might be considered as waves. His inspiration was Einstein’s discovery, made some two decades previously, that light—traditionally thought of as a wave—could also be a particle, dubbed a light quantum. Perhaps electrons as well as light might be both wave and particle at the same time—simply beyond imaginable.
In spring 1926, the flamboyant Erwin Schrödinger, at the University of Zürich, burst on the scene. At thirty-nine, Schrödinger was an outsider in age, temperament, and thought to the group of impetuous twenty-something quantum physicists who clustered around Bohr in Copenhagen, Sommerfeld in Munich, and Born in Göttingen.
Schrödinger had found the equation that converted de Broglie’s vision of matter as waves into a coherent theory. His version of atomic physics, which he called wave mechanics, was based on treating light and electrons as waves. “My theory was inspired by L. de Broglie,” he wrote. “No genetic relation whatever with Heisenberg is known to me. I knew of his theory, of course, but felt discouraged, not to say repelled, by the methods of the transcendental algebra, which appeared very difficult to me, and by the lack of visualizability.”
Schrödinger’s wave mechanics sprang from a preference for a mathematics that was more familiar and beautiful, as opposed to what he referred to as Heisenberg’s ugly “transcendental algebra.” The “Schrödinger equation” offered great advantages in calculations over Heisenberg’s quantum mechanics, added to which it enabled the electron in an atom to be visualized as a wave surrounding the nucleus. It had taken Pauli twenty-odd pages to solve the hydrogen atom problem. Schrödinger did it in a page.
Schrödinger pointed out that the wave nature of matter promised a return to classical continuity. The passage of an electron between stationary states could be envisioned as a string passing continuously from one mode of oscillation to another.
One year earlier there had been no viable atomic theory. Now there were two: Heisenberg’s quantum mechanics and Schrödinger’s wave mechanics.
Heisenberg was furious about Schrödinger’s work and even more so about its rave reviews from the physics community. “The more I reflect on the physical portion of Schrödinger’s theory, the more disgusting I find it,” he wrote to Pauli. “What Schrödinger writes on the visualizability of his theory I consider crap.”
Heisenberg saw wave functions—that is, the solutions to Schrödinger’s wave equation—as nothing more than a means to expedite calculations. To demonstrate this he applied them to the problem that had driven Born, Pauli, and himself to despair: to find a mathematical way to describe the properties of the helium atom. No one had been able to deduce stable orbits, or stationary states, for the two electrons in the helium atom using Bohr’s theory of the atom. This being the case, they could not move on to deduce spectral lines for the helium atom because these resulted from its electrons dropping down from a higher to a lower orbit. Instead, the electrons’ orbits remained unstable, meaning that an electron could be knocked out of the helium atom by the smallest of disturbances.
But in Heisenberg’s quantum mechanics there were no orbits. The problem became one of deducing the atom’s spectral lines from its stationary states expressed directly in terms of the electrons’ energy and momentum in the atom. If the spectral lines turned out to be wrong, it would show that there were serious problems with the way quantum mechanics defined stationary states, that is, the energy levels of electrons in atoms. The spectral lines of the helium atom were particularly interesting to physicists because, as had been observed in the laboratory, they fell into two distinct groups. But why