A potential energy surface is generally used in quantum mechanics and statistical mechanics to model reactions and interactions in simple chemical and physical systems. There is a natural correspondence between potential energy surfaces as they exist (as polynomial surfaces) and their application in potential theory, which associates and studies harmonic functions in relation to these surfaces.

For example, the Morse potential and the simple harmonic potential well are common in applications of quantum chemistry and physics. Before quantum field theory, this approach was representative of research conducted in quantum mechanics.