This computes the interaction energy between a point charge "q" and a "flat" metal surface, when the charge is at a distance "x" from the surface. Owing to the method of its derivation, this interaction is called the "image potential energy" (image PE). Schottky based his work on earlier work by Lord Kelvin relating to the image PE for a sphere. Schottky's image PE has become a standard component in simple models of the barrier to motion, "M"("x"), experienced by an electron on approaching a metal surface or a metal–semiconductor interface from the inside. (This "M"("x") is the quantity that appears when the one-dimensional, one-particle, Schrödinger equation is written in the form