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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2309.06044 |
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| _version_ | 1866914633031352320 |
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| author | Acar, Yiğit Can Acevedo, Lorena Kuru, Şengül |
| author_facet | Acar, Yiğit Can Acevedo, Lorena Kuru, Şengül |
| contents | In this paper, we search the factorizations of the shape invariant Hamiltonians with Scarf II potential. We find two classes; one of them is the standard real factorization which leads us to a real hierarchy of potentials and their energy levels; the other one is complex and it leads us naturally to a hierarchy of complex Hamiltonians. We will show some properties of these complex Hamiltonians: they are not parity-time (or PT) symmetric, but their spectrum is real and isospectral to the Scarf II real Hamiltonian hierarchy. The algebras for real and complex shift operators (also called potential algebras) are computed; they consist of $su(1,1)$ for each of them and the total potential algebra including both hierarchies is the direct sum $su(1,1)\oplus su(1,1)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_06044 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Unusual isospectral factorizations of shape invariant Hamiltonians with Scarf II potential Acar, Yiğit Can Acevedo, Lorena Kuru, Şengül Mathematical Physics 81Q60 In this paper, we search the factorizations of the shape invariant Hamiltonians with Scarf II potential. We find two classes; one of them is the standard real factorization which leads us to a real hierarchy of potentials and their energy levels; the other one is complex and it leads us naturally to a hierarchy of complex Hamiltonians. We will show some properties of these complex Hamiltonians: they are not parity-time (or PT) symmetric, but their spectrum is real and isospectral to the Scarf II real Hamiltonian hierarchy. The algebras for real and complex shift operators (also called potential algebras) are computed; they consist of $su(1,1)$ for each of them and the total potential algebra including both hierarchies is the direct sum $su(1,1)\oplus su(1,1)$. |
| title | Unusual isospectral factorizations of shape invariant Hamiltonians with Scarf II potential |
| topic | Mathematical Physics 81Q60 |
| url | https://arxiv.org/abs/2309.06044 |