This paper uses the newly developed quantum action-angle variable formalism to reduce the Schrödinger equation for the three atom system to the minimum number of coordinates, four. A transformation is also presented which converts the operator to a form amenable to conventional direct numerical integration techniques. Computational considerations relevant to the application of finite elements are discussed, and these are illustrated with a numerical calculation of the quantum energy levels of a rigid asymmetric rotor. The ordinary differential equation which is derived for the last problem permits an unambiguous assignment of the correct expression for the total angular momentum, and the result is different from that used in previous semiclassical calculations.
All Science Journal Classification (ASJC) codes
- Physics and Astronomy(all)
- Physical and Theoretical Chemistry