H(Ψn = Ψn(0) + λ Ψn(1) + λ2Ψn(2) + λ3Ψn(3) …) =
(En(0) + λ En(1) + λ2En(2) + λ3En(3) …) Ψn(9)
The first order and higher order variations or corrections to the wave function and to the energy are obtained, by solving equation (9) and analyzing the terms (Griffith, 1994; Liboff, 2002; Reed, 2007).