From orbits to orbitals. Early pictorializations of electron probability densities

The transition from atomic models of the old quantum theory to the wave mechanics of mature quantum mechanics entailed a change from electronic orbits to orbitals. The former look like planets orbiting a central star, while orbitals are electronic wave functions interpreted as probability densities. In this paper, we investigate early attempts to create pictorial images of the electronic probability density in the hydrogen atom. We analyse various approaches to visualize solutions to the Schrödinger equation for atomic hydrogen from first attempts in the early 1930s until the advent of modern computer graphics in the 1970s. We replicate the approaches by White (1931), DeVault (1944) and Wiswesser (1945) and discuss their intrinsic features and limitations. The translation of abstract mathematical probability densities into tangible and broadly accessible pictorial representations of orbitals is a complex process that critically depends on the concepts and tools available for graphical representation.