To Explain the World: The Discovery of Modern Science

by Steven Weinberg

These early steps were followed in the 1920s with the development of general rules of quantum mechanics, rules that can be applied to any physical system. This was chiefly the work of Louis de Broglie, Werner Heisenberg, Wolfgang Pauli, Pascual Jordan, Erwin Schrödinger, Paul Dirac, and Max Born. The energies of allowed atomic states are calculated by solving an equation, the Schrödinger equation, of a general mathematical type that was already familiar from the study of sound and light waves. A string on a musical instrument can produce just those tones for which a whole number of half wavelengths fit on the string; analogously, Schrödinger found that the allowed energy levels of an atom are those for which the wave governed by the Schrödinger equation just fits around the atom without discontinuities. But as first recognized by Born, these waves are not waves of pressure or of electromagnetic fields, but waves of probability—a particle is most likely to be near where the wave function is largest.