### Abstract

Original language | English |
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Title of host publication | Trends in Mathematics |

Pages | 9-19 |

Number of pages | 11 |

Publication status | Published - 2019 |

### Publication series

Name | TRENDS IN MATHEMATICS |
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### Fingerprint

### All Science Journal Classification (ASJC) codes

- Mathematics(all)

### Cite this

*Trends in Mathematics*(pp. 9-19). (TRENDS IN MATHEMATICS).

**Two-dimensional noncommutative swanson model and its bicoherent states.** / Spagnolo, Salvatore; Gargano, Francesco; Bagarello, Fabio; Bagarello, Fabio.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

*Trends in Mathematics.*TRENDS IN MATHEMATICS, pp. 9-19.

}

TY - CHAP

T1 - Two-dimensional noncommutative swanson model and its bicoherent states

AU - Spagnolo, Salvatore

AU - Gargano, Francesco

AU - Bagarello, Fabio

AU - Bagarello, Fabio

PY - 2019

Y1 - 2019

N2 - We introduce an extended version of the Swanson model, defined on a two-dimensional noncommutative space, which can be diagonalized exactly by making use of pseudo-bosonic operators. Its eigenvalues are explicitly computed and the biorthogonal sets of eigenstates of the Hamiltonian and of its adjoint are explicitly constructed.We also show that it is possible to construct two displacement-like operators from which a family of bi-coherent states can be obtained. These states are shown to be eigenstates of the deformed lowering operators, and their projector allows to produce a suitable resolution of the identity in a dense subspace of L 2 (R 2 ).

AB - We introduce an extended version of the Swanson model, defined on a two-dimensional noncommutative space, which can be diagonalized exactly by making use of pseudo-bosonic operators. Its eigenvalues are explicitly computed and the biorthogonal sets of eigenstates of the Hamiltonian and of its adjoint are explicitly constructed.We also show that it is possible to construct two displacement-like operators from which a family of bi-coherent states can be obtained. These states are shown to be eigenstates of the deformed lowering operators, and their projector allows to produce a suitable resolution of the identity in a dense subspace of L 2 (R 2 ).

KW - Coherent states

KW - Mathematics (all)

KW - Pseudo-bosons

KW - Swanson model

UR - http://hdl.handle.net/10447/353331

UR - http://www.springer.com/series/4961

M3 - Chapter

SN - 978-3-030-01155-0

T3 - TRENDS IN MATHEMATICS

SP - 9

EP - 19

BT - Trends in Mathematics

ER -