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 ).
Bagarello, F., Gargano, F., Spagnolo, S. (2019). Two-dimensional noncommutative swanson model and its bicoherent states. In Trends in Mathematics (pp. 9-19). Springer International Publishing [10.1007/978-3-030-01156-7_2].
Two-dimensional noncommutative swanson model and its bicoherent states
Bagarello, Fabio;Gargano, Francesco;Spagnolo, Salvatore
2019-01-01
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 ).
| File | Dimensione | Formato | |
|---|---|---|---|
|
2019_BGS_Trends.pdf
Solo gestori archvio
Dimensione
4.63 MB
Formato
Adobe PDF
|
4.63 MB | Adobe PDF | Visualizza/Apri Richiedi una copia |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
