dorsal/arxiv
View SchemaGreen's matrix from Jacobi-matrix Hamiltonian
| Authors | B. Kónya, G. Lévai, Z. Papp |
|---|---|
| Categories | |
| ArXiv ID | physics/9704025 |
| URL | https://arxiv.org/abs/physics/9704025 |
| DOI | 10.1063/1.532127 |
| Journal | J.Math.Phys. 38 (1997) 4832-4844 |
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 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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"abstract": "We propose two ways for determining the Green\u0027s matrix for problems admitting\nHamiltonians that have infinite symmetric tridiagonal (i.e. Jacobi) matrix form\non some basis representation. In addition to the recurrence relation comming\nfrom the Jacobi-matrix, the first approach also requires the matrix elements of\nthe Green\u0027s operator between the first elements of the basis. In the second\napproach the recurrence relation is solved directly by continued fractions and\nthe solution is continued analytically to the whole complex plane. Both\napproaches are illustrated with the non-trivial but calculable example of the\nD-dimensional Coulomb Green\u0027s matrix. We give the corresponding formulas for\nthe D-dimensional harmonic oscillator as well.",
"arxiv_id": "physics/9704025",
"authors": [
"B. K\u00f3nya",
"G. L\u00e9vai",
"Z. Papp"
],
"categories": [
"math-ph",
"math.MP"
],
"doi": "10.1063/1.532127",
"journal_ref": "J.Math.Phys. 38 (1997) 4832-4844",
"title": "Green\u0027s matrix from Jacobi-matrix Hamiltonian",
"url": "https://arxiv.org/abs/physics/9704025"
},
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