Green's matrix from Jacobi-matrix Hamiltonian

Details Green's matrix from Jacobi-matrix Hamiltonian Green's matrix from Jacobi-matrix Hamiltonian

1997-04-20

arxiv.org/abs/physics/9704025v1

J.Math.Phys. 38 (1997) 4832-4844

Physics

Mathematical Physics

16 pages revtex, to be published in Journal of Mathematical Physics

Scientific paper

10.1063/1.532127

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 comming 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.

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