|
Эта публикация цитируется в 2 научных статьях (всего в 2 статьях)
Ladder Operators and Hidden Algebras for Shape Invariant Nonseparable and Nondiagonalizable Models with Quadratic Complex Interaction. II. Three-Dimensional Model
Ian Marquettea, Christiane Quesneb a School of Mathematics and Physics, The University of Queensland,
Brisbane, QLD 4072, Australia
b Physique Nucléaire Théorique et Physique Mathématique, Université Libre de Bruxelles, Campus de la Plaine CP229, Boulevard du Triomphe, B-1050 Brussels, Belgium
Аннотация:
A shape invariant nonseparable and nondiagonalizable three-dimensional model with quadratic complex interaction was introduced by Bardavelidze, Cannata, Ioffe, and Nishnianidze. However, the complete hidden symmetry algebra and the description of the associated states that form Jordan blocks remained to be studied. We present a set of six operators $\{A^{\pm},B^{\pm},C^{\pm}\}$ that can be combined to build a ${\mathfrak{gl}}(3)$ hidden algebra. The latter can be embedded in an ${\mathfrak{sp}}(6)$ algebra, as well as in an ${\mathfrak{osp}}(1/6)$ superalgebra. The states associated with the eigenstates and making Jordan blocks are induced in different ways by combinations of operators acting on the ground state. We present the action of these operators and study the construction of an extended biorthogonal basis. These rely on establishing various nontrivial polynomial and commutator identities. We also make a connection between the hidden symmetry and the underlying superintegrability property of the model. Interestingly, the integrals generate a cubic algebra. This work demonstrates how various concepts that have been applied widely to Hermitian Hamiltonians, such as hidden symmetries, superintegrability, and ladder operators, extend to the pseudo-Hermitian case with many differences.
Ключевые слова:
quantum mechanics, complex potentials, pseudo-Hermiticity, Lie algebras, Lie superalgebras.
Поступила: 1 сентября 2021 г.; в окончательном варианте 3 января 2022 г.; опубликована 14 января 2022 г.
Образец цитирования:
Ian Marquette, Christiane Quesne, “Ladder Operators and Hidden Algebras for Shape Invariant Nonseparable and Nondiagonalizable Models with Quadratic Complex Interaction. II. Three-Dimensional Model”, SIGMA, 18 (2022), 005, 24 pp.
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/sigma1800 https://www.mathnet.ru/rus/sigma/v18/p5
|
Статистика просмотров: |
Страница аннотации: | 64 | PDF полного текста: | 21 | Список литературы: | 12 |
|