GREENS MATRIX FROM JACOBI-MATRIX HAMILTONIAN

We propose two ways for determining the Green's matrix for problems ad mitting Hamiltonians that have infinite symmetric tridiagonal (i.e., J acobi) matrix form on some basis representation, Tn addition to the re currence relation coming from the Jacobi-matrix, the first approach al so requires the matrix elements of the Green's operator between the fi rst elements of the basis. In the second approach the recurrence relat ion is solved directly by continued fractions and the solution is cont inued analytically to the whole complex plane. Both approaches are ill ustrated with the non-trivial but calculable example of the D-dimensio nal Coulomb Green's matrix. We give the corresponding formulas for the D-dimensional harmonic oscillator as well. (C) 1997 American Institut e of Physics.