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Gómez-Ullate Otaiza, David and Kamran, Niky and Milson, Robert
(2004)
*The Darboux transformation and algebraic deformations of shape-invariant potentials.*
Journal of physics A: Mathematical and general, 37
(5).
pp. 1789-1804.
ISSN 0305-4470

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Official URL: http://dx.doi.org/10.1088/0305-4470/37/5/022

## Abstract

We investigate the backward Darboux transformations (addition of the lowest bound state) of shape-invariant potentials on the line, and classify the subclass of algebraic deformations, those for which the potential and the bound states are simple elementary functions. A countable family, m = 0, 1,.2,..., of deformations exists for each family of shape-invariant potentials. We prove that the m_th deformation is exactly solvable by polynomials, meaning that it leaves invariant an infinite flag of polynomial modules P_(m)^(m) Ϲ P_(-m+1)^(m) Ϲ (...) , where P_n^(m) is a codimension m subspace of <1, z,..., z_(n)>. In particular, we prove that the first (m = 1) algebraic deformation of the shape-invariant class is precisely the class of operators preserving the infinite flag of exceptional monomial modules P_n^(1) = <1, z_(2),..., z_(n)>. By construction, these algebraically deformed Hamiltonians do not have an sl(2) hidden symmetry algebra structure.

Item Type: | Article |
---|---|

Additional Information: | ©Iop science. |

Uncontrolled Keywords: | Differential-operators; Schrodinger-operators; Factorization method; Quantum-mechanics; Supersymmetry; Equation |

Subjects: | Sciences > Physics > Physics-Mathematical models Sciences > Physics > Mathematical physics |

ID Code: | 30915 |

Deposited On: | 17 Jun 2015 14:02 |

Last Modified: | 10 Dec 2018 15:09 |

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