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Singular Eigenfunctions of Calogero-Sutherland Type Systems and How to Transform Them into Regular Ones
KTH, Skolan för teknikvetenskap (SCI), Teoretisk fysik.
2007 (Engelska)Ingår i: SIGMA. Symmetry, Integrability and Geometry, ISSN 1815-0659, E-ISSN 1815-0659, Vol. 3, s. 031-Artikel i tidskrift (Refereegranskat) Published
Abstract [en]

There 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.

Ort, förlag, år, upplaga, sidor
2007. Vol. 3, s. 031-
Nyckelord [en]
quantum integrable systems, orthogonal polynomials, singular eigenfunctions
Nationell ämneskategori
Fysik
Identifikatorer
URN: urn:nbn:se:kth:diva-37058ISI: 000207065200031Scopus ID: 2-s2.0-84889234831OAI: oai:DiVA.org:kth-37058DiVA, id: diva2:431937
Tillgänglig från: 2011-07-27 Skapad: 2011-07-27 Senast uppdaterad: 2017-12-08Bibliografiskt granskad

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Langmann, Edwin
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