Singular Eigenfunctions of Calogero-Sutherland Type Systems and How to Transform Them into Regular Ones
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Singular Eigenfunctions of Calogero-Sutherland Type Systems and How to Transform Them into Regular Ones
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| Creator |
Langmann, E.
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| Description |
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.
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| Date |
2019-02-16T08:08:16Z
2019-02-16T08:08:16Z 2007 |
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| Type |
Article
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| Identifier |
Singular Eigenfunctions of Calogero-Sutherland Type Systems and How to Transform Them into Regular Ones / E. Langmann // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 26 назв. — англ.
1815-0659 2000 Mathematics Subject Classification: 81U15; 33C50; 05E05 http://dspace.nbuv.gov.ua/handle/123456789/147783 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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