Singular Eigenfunctions of Calogero-Sutherland Type Systems and How to Transform Them into Regular Ones

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dc.creatorLangmann, Edwin
dc.date2007-02-26
dc.date.accessioned2026-07-07T09:34:28Z
dc.date.available2026-07-07T09:34:28Z
dc.descriptionThere exists a large class of quantum many-body systems of Calogero-Sutherland type where all particles can have different masses and coupling constants and which nevertheless are such that one can construct a complete (in a certain sense) set of exact eigenfunctions and corresponding eigenvalues, explicitly. Of course there is a catch to this result: if one insists on these eigenfunctions to be square integrable then the corresponding Hamiltonian is necessarily non-hermitean (and thus provides an example of an exactly solvable PT-symmetric quantum-many body system), and if one insists on the Hamiltonian to be hermitean then the eigenfunctions are singular and thus not acceptable as quantum mechanical eigenfunctions. The standard Calogero-Sutherland Hamiltonian is special due to the existence of an integral operator which allows to transform these singular eigenfunctions into regular ones.
dc.descriptionThis is a contribution to the Vadim Kuznetsov Memorial Issue on Integrable Systems and Related Topics, published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/
dc.identifierhttps://arxiv.org/abs/math-ph/0702089
dc.identifierhttp://arxiv.org/abs/math-ph/0702089
dc.identifierSIGMA 3 (2007), 031, 18 pages
dc.identifierdoi:10.3842/SIGMA.2007.031
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/159501
dc.subjectMathematical Physics
dc.subjectExactly Solvable and Integrable Systems
dc.titleSingular Eigenfunctions of Calogero-Sutherland Type Systems and How to Transform Them into Regular Ones
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