A free-electron theory of optical activity

The Schrödinger equation is derived for an electron moving in the field of a potential supported by a space curve, and an approximate solution is found which becomes exact as the potential binds the electron more and more tightly to the curve but otherwise does not restrict the electron's motion along the curve. These so-called free-electron wavefunctions and energy levels are used to obtain a general expression for the optical rotatory power associated with an arbitrary space curve. Calculations of the specific rotatory power are carried out for three different curves.