Green's operator for Hamiltonians with Coulomb plus polynomial potentials

Details Green's operator for Hamiltonians with Coulomb plus polynomial potentials Green's operator for Hamiltonians with Coulomb plus polynomial potentials

2006-12-16

arxiv.org/abs/math-ph/0612053v1

Physics

Mathematical Physics

4 pages

Scientific paper

10.1088/1751-8113/40/27/020

The Hamiltonian of a Coulomb plus polynomial potential on the Coulomb-Sturmian basis has an infinite symmetric band-matrix structure. A band matrix can always be considered as a block-tridiagonal matrix. So, the corresponding Green's operator can be given as a matrix-valued continued fraction. As examples, we calculate the Green's operator for the Coulomb plus linear and quadratic potential problems and determine the energy levels.

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