N. Bessis et G. Bessis, PERTURBATION-THEORY USING SERIES EXPANSIONS AND THE RICCATI EQUATION, The Journal of chemical physics, 103(8), 1995, pp. 3006-3013
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.