Abstract
Abstract We generalize the Rayleigh-Schrodinger perturbation formalism to the hamiltonians H = H 0 + λH 1 where the correction λH 1 is small and the unperturbed operator H 0 is represented by an infinite tridiagonal matrix. This enables us to construct the solutions E = E 0 + λE 1 + λ 2 E 2 +… and | ψ 〉 = | ψ 0 〉+ λ | ψ 1 〉+ λ 2 | ψ 2 〉+… in terms of the analytic continued fractions.
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