Dreams of a Final Theory: The Scientist's Search for the Ultimate Laws of Nature

by Steven Weinberg

At the heart of Schrödinger’s approach was a dynamical equation (known ever since as the Schrödinger equation) that dictated the way that any given particle wave would change with time. Some of the solutions of the Schrödinger equation for electrons in atoms simply oscillate at a single pure frequency, like the sound wave produced by a perfect tuning fork. Such special solutions correspond to the possible stable quantum states of the atom or molecule (something like the stable waves of vibration within a tuning fork), with the energy of the atomic state given by the frequency of the wave times Planck’s constant. These are the energies that are revealed to us through the colors of the light that the atom can emit or absorb. The Schrödinger equation is mathematically the same sort of equation (known as a partial differential equation) that had been used since the nineteenth century to study waves of sound or light. Physicists in the 1920s were already so comfortable with this sort of wave equation that they were able immediately to set about calculating the energies and other properties of all sorts of atoms and molecules. It was a golden time for physics. Other successes followed rapidly, and one by one the mysteries that had surrounded atoms and molecules seemed to melt away.