In 1925, following the suggestions of French physicist Louis Victor de Broglie that matter particles could behave like waves, Austrian physicist Erwin Schrödinger advanced a differential wave equation to describe particles such as electrons. Schrödinger's equation is given schematically by H(psi) = E(psi), where E is simply a number describing the energy of the electron, and H is a mathematical operator known as the Hamiltonian, containing derivative and multiplicative operators. The solution of Schrödinger's equation in simple cases leads to interesting predictions. For example, if electrons are confined to a box, or potential well, the energy states are quantized, meaning the energy may only have certain discrete values. Schrödinger solved his equation for the hydrogen atom and discovered that the energies given by its solution matched the observable hydrogen spectra.

Schrödinger and other physicists, however, were...