Green's matrix from Jacobi-matrix Hamiltonian

B. Kónya, G. Lévai, Z. Papp

Research output: Contribution to journalArticle

18 Citations (Scopus)

Abstract

We propose two ways for determining the Green's matrix for problems admitting Hamiltonians that have infinite symmetric tridiagonal (i.e., Jacobi) matrix form on some basis representation. In addition to the recurrence relation coming from the Jacobi-matrix, the first approach also requires the matrix elements of the Green's operator between the first elements of the basis. In the second approach the recurrence relation is solved directly by continued fractions and the solution is continued analytically to the whole complex plane. Both approaches are illustrated with the non-trivial but calculable example of the D-dimensional Coulomb Green's matrix. We give the corresponding formulas for the D-dimensional harmonic oscillator as well.

Original languageEnglish
Pages (from-to)4832-4844
Number of pages13
JournalJournal of Mathematical Physics
Volume38
Issue number9
DOIs
Publication statusPublished - Sep 1997

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ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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