PERTURB: A program for calculating vibrational energies by generalized algebraic quantization

Abstract

We describe PERTURB, a special purpose algebraic manipulation program which calculates vibrational eigenvalues in coupled oscillator systems. PERTURB implements the method of generalized algebraic quantization (AQ), in which Van Vleck perturbation theory is formulated in a mock phase space. The phase space formulation enables quantum and classical perturbation theory to be treated on the same footing, and allows the systematic calculation of corrections to classical perturbation results in powers of h ̷ . Generalized AQ is a powerful and efficient technique for calculating semiclassical vibrational energy levels. In many cases, including just the first correction to classical perturbation theory yields highly accurate energies.