PERTURBATION-THEORY USING SERIES EXPANSIONS AND THE RICCATI EQUATION

An algebraic procedure is proposed for the analytical solution of Schr odinger equations that can be viewed as a factorizable equation with a n adequately chosen perturbation. This procedure relies on the solutio n of the Riccati equation associated with the given eigenequation and the use of power series of suitable functions which are specific to ea ch factorization type. As illustrative examples, analytical solution o f the symmetric anharmonic oscillator, perturbed Morse oscillator and singular anharmonic oscillator equations are carried out. Further appl ications are pointed out. (C) 1995 American Institute of Physics.