dorsal/arxiv
View SchemaClosed form representation for a projection onto infinitely dimensional subspace spanned by Coulomb bound states
| Authors | O. M. Deryuzhkova, S. B. Levin, S. L. Yakovlev |
|---|---|
| Categories | |
| ArXiv ID | physics/0608245 |
| URL | https://arxiv.org/abs/physics/0608245 |
| DOI | 10.1088/0953-4075/39/22/019 |
| Journal | , J. Phys. B: At. Mol. Opt. Phys. 39 (2006) 4767-4773 |
Abstract
The closed form integral representation for the projection onto the subspace spanned by bound states of the two-body Coulomb Hamiltonian is obtained. The projection operator onto the $n^2$ dimensional subspace corresponding to the $n$-th eigenvalue in the Coulomb discrete spectrum is also represented as the combination of Laguerre polynomials of $n$-th and $(n-1)$-th order. The latter allows us to derive an analog of the Christoffel-Darboux summation formula for the Laguerre polynomials. The representations obtained are believed to be helpful in solving the breakup problem in a system of three charged particles where the correct treatment of infinitely many bound states in two body subsystems is one of the most difficult technical problems.
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"abstract": "The closed form integral representation for the projection onto the subspace\nspanned by bound states of the two-body Coulomb Hamiltonian is obtained. The\nprojection operator onto the $n^2$ dimensional subspace corresponding to the\n$n$-th eigenvalue in the Coulomb discrete spectrum is also represented as the\ncombination of Laguerre polynomials of $n$-th and $(n-1)$-th order. The latter\nallows us to derive an analog of the Christoffel-Darboux summation formula for\nthe Laguerre polynomials. The representations obtained are believed to be\nhelpful in solving the breakup problem in a system of three charged particles\nwhere the correct treatment of infinitely many bound states in two body\nsubsystems is one of the most difficult technical problems.",
"arxiv_id": "physics/0608245",
"authors": [
"O. M. Deryuzhkova",
"S. B. Levin",
"S. L. Yakovlev"
],
"categories": [
"physics.atom-ph"
],
"doi": "10.1088/0953-4075/39/22/019",
"journal_ref": ", J. Phys. B: At. Mol. Opt. Phys. 39 (2006) 4767-4773",
"title": "Closed form representation for a projection onto infinitely dimensional subspace spanned by Coulomb bound states",
"url": "https://arxiv.org/abs/physics/0608245"
},
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