Particle in a one-dimensional lattice

In the Kronig - Penney model ( according to Ralph Kronig and William Penney ) is a simple model of solid-state physics that explains the behavior of valence electrons in crystalline solids. From it there is a band structure of the energy, as it occurs in nature, similar to, for example, metals and semiconductors.

Explanation

The one-dimensional model is based on a sequence of potential wells of depth U0, each of a wide and b separated by a barrier of width. The pots represent the portion in the vicinity of the atomic nuclei, in which the electrons are attracted by the core charge. The barrier correspond to lying between the core regions in which the charge of the core is shielded by the core electrons. The grid is infinitely extended and after the Bloch theorem spatially periodic solutions of the Schrödinger equation arise. Substituting these conditions, so resulting energy bands separated by forbidden energy ranges. It can not exist electrons with energies from the prohibited areas in the crystal, with energies from the energy bands.

Form at the boundary between allowed and forbidden energy regions on the basis of Bragg reflection standing waves. The standing waves in which the electrons prefer to stay near atomic nuclei, are energetically more favorable than those of standing waves in which electrons tend to stay between atomic nuclei. The Bragg reflection from the periodic potential can therefore be considered as the cause of the forbidden energy ranges.