Singular Eigenfunctions of Calogero-Sutherland Type Systems and How to Transform Them into Regular Ones
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, e...
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| Дата: | 2007 |
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| Формат: | Стаття |
| Мова: | English |
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Інститут математики НАН України
2007
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/147783 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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irk-123456789-1477832019-02-17T01:24:42Z Singular Eigenfunctions of Calogero-Sutherland Type Systems and How to Transform Them into Regular Ones Langmann, E. 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. 2007 Article 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 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Langmann, E. |
| spellingShingle |
Langmann, E. Singular Eigenfunctions of Calogero-Sutherland Type Systems and How to Transform Them into Regular Ones Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Langmann, E. |
| author_sort |
Langmann, E. |
| title |
Singular Eigenfunctions of Calogero-Sutherland Type Systems and How to Transform Them into Regular Ones |
| title_short |
Singular Eigenfunctions of Calogero-Sutherland Type Systems and How to Transform Them into Regular Ones |
| title_full |
Singular Eigenfunctions of Calogero-Sutherland Type Systems and How to Transform Them into Regular Ones |
| title_fullStr |
Singular Eigenfunctions of Calogero-Sutherland Type Systems and How to Transform Them into Regular Ones |
| title_full_unstemmed |
Singular Eigenfunctions of Calogero-Sutherland Type Systems and How to Transform Them into Regular Ones |
| title_sort |
singular eigenfunctions of calogero-sutherland type systems and how to transform them into regular ones |
| publisher |
Інститут математики НАН України |
| publishDate |
2007 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/147783 |
| citation_txt |
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. |
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Symmetry, Integrability and Geometry: Methods and Applications |
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