Two-dimensional noncommutative swanson model and its bicoherent states

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

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 ).
Original languageEnglish
Title of host publicationTrends in Mathematics
Pages9-19
Number of pages11
Publication statusPublished - 2019

Publication series

NameTRENDS IN MATHEMATICS

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Operator
Projector
Coherent States
Subspace
Model
Eigenvalue
Family

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

Spagnolo, S., Gargano, F., Bagarello, F., & Bagarello, F. (2019). Two-dimensional noncommutative swanson model and its bicoherent states. In 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.

Trends in Mathematics. 2019. p. 9-19 (TRENDS IN MATHEMATICS).

Research output: Chapter in Book/Report/Conference proceedingChapter

Spagnolo, S, Gargano, F, Bagarello, F & Bagarello, F 2019, Two-dimensional noncommutative swanson model and its bicoherent states. in Trends in Mathematics. TRENDS IN MATHEMATICS, pp. 9-19.
Spagnolo S, Gargano F, Bagarello F, Bagarello F. Two-dimensional noncommutative swanson model and its bicoherent states. In Trends in Mathematics. 2019. p. 9-19. (TRENDS IN MATHEMATICS).
Spagnolo, Salvatore ; Gargano, Francesco ; Bagarello, Fabio ; Bagarello, Fabio. / Two-dimensional noncommutative swanson model and its bicoherent states. Trends in Mathematics. 2019. pp. 9-19 (TRENDS IN MATHEMATICS).
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