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This article is cited in 4 scientific papers (total in 4 papers)
Singular Eigenfunctions of Calogero–Sutherland Type Systems and How to Transform Them into Regular Ones
Edwin Langmann Theoretical Physics, KTH Physics, AlbaNova, SE-106 91 Stockholm, Sweden
Abstract:
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 $\mathcal{PT}$-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.
Keywords:
quantum integrable systems; orthogonal polynomials; singular eigenfunctions.
Received: November 2, 2006; in final form January 29, 2007; Published online February 26, 2007
Citation:
Edwin Langmann, “Singular Eigenfunctions of Calogero–Sutherland Type Systems and How to Transform Them into Regular Ones”, SIGMA, 3 (2007), 031, 18 pp.
Linking options:
https://www.mathnet.ru/eng/sigma157 https://www.mathnet.ru/eng/sigma/v3/p31
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Abstract page: | 178 | Full-text PDF : | 48 | References: | 24 |
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