Наукова електронна бібліотека
періодичних видань НАН України
періодичних видань НАН України
Revisiting the Symmetries of the Quantum Smorodinsky-Winternitz System in D Dimensions
Репозиторій DSpace/Manakin
- Домашня сторінка
- →
- Фізико-технічні та математичні науки
- →
- Відділення математики
- →
- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
- →
- Symmetry, Integrability and Geometry: Methods and Applications, 2011, том 7
- →
- Symmetry, Integrability and Geometry: Methods and Applications, 2011, том 7, випуск за цей рік
- →
- Переглянути статтю
JavaScript is disabled for your browser. Some features of this site may not work without it.
Revisiting the Symmetries of the Quantum Smorodinsky-Winternitz System in D Dimensions
Інший ID:
2010 Mathematics Subject Classification: 20C35; 81R05; 81R12
DOI:10.3842/SIGMA.2011.035
DOI:10.3842/SIGMA.2011.035
Посилання:
Revisiting the Symmetries of the Quantum Smorodinsky-Winternitz System in D Dimensions / C. Quesne // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 90 назв. — англ.
Підтримка:
This paper is a contribution to the Special Issue “Symmetry, Separation, Super-integrability and Special Functions (S4)”. The full collection is available at http://www.emis.de/journals/SIGMA/S4.html.
Дата:
2011
Переглядів:
561
Завантажень:
274
Анотація:
The D-dimensional Smorodinsky-Winternitz system, proposed some years ago by Evans, is re-examined from an algebraic viewpoint. It is shown to possess a potential algebra, as well as a dynamical potential one, in addition to its known symmetry and dynamical algebras. The first two are obtained in hyperspherical coordinates by introducing D auxiliary continuous variables and by reducing a 2D-dimensional harmonic oscillator Hamiltonian. The su(2D) symmetry and w(2D)⊕s sp(4D,R) dynamical algebras of this Hamiltonian are then transformed into the searched for potential and dynamical potential algebras of the Smorodinsky-Winternitz system. The action of generators on wavefunctions is given in explicit form for D=2.
