ABSTRACT

This chapter discusses the inversion of the Schrödinger matrix by the Padé–Lanczos approximant (PLA). It shows the construction of the Green function by using the Lanczos representation for the Schrödinger matrix within the infinite chain model. The determinant of the Green function can be computed iteratively by expressing it in terms of its subdeterminants via the usage of the Cauchy expansion for determinants. The chapter demonstrates that the explicit and exact inversion of scaled evolution matrix is possible for any finite rank and the analytical result is precisely the PLA.