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Green's operator for Hamiltonians with Coulomb plus polynomial potentials

E. Kelbert·A. Hyder·F. Demir·Z. T. Hlousek·Z. Papp
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Abstract

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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E. Kelbert, A. Hyder, F. Demir, Z. T. Hlousek, Z. Papp. 2006-12-16. Green's operator for Hamiltonians with Coulomb plus polynomial potentials. https://doi.org/10.1088/1751-8113/40/27/020

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