PERTURBATION THEORY USING SERIES EXPANSIONS AND THE RICCATI EQUATION

摘要

An algebraic procedure is proposed for the analytical solution of Schrodinger equations that can be viewed as a factorizable equation with an adequately chosen perturbation. This procedure relies on the solution of the Riccati equation associated with the given eigenequation and the use of power series of suitable functions which are specific to each factorization type. As illustrative examples, analytical solution of the symmetric anharmonic oscillator, perturbed Morse oscillator and singular anharmonic oscillator equations are carried out. Further applications are pointed out. (C) 1995 American Institute of Physics. [References: 17]