A one-dimensional model of electrons in crystals in which the periodic potential of a potential is represented by an infinite array of regularly spaced rectangular potentials. This model was proposed and solved by Ralph Kronig (1904–95) and William Penney (1909–91) in 1931. The Kronig–Penney model gives considerable insight into energy bands. It has since been extended to discuss impurity states, surface states, and disordered solids.