6533b853fe1ef96bd12ad646

RESEARCH PRODUCT

Two-dimensional Noncommutative Swanson Model and Its Bicoherent States

Francesco GarganoFabio BagarelloSalvatore Spagnolo

subject

Pseudo-bosonPhysicsSwanson modelNoncommutative geometrylaw.inventionsymbols.namesakeProjectorlawBiorthogonal systemsymbolsMathematics (all)Coherent statesHamiltonian (quantum mechanics)Coherent stateEigenvalues and eigenvectorsSubspace topologyMathematical physics

description

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 \(\mathcal{L}^\mathrm{2}\, (\mathbb{R}^\mathrm{2})\).

yearjournalcountryeditionlanguage
2019-01-01
https://doi.org/10.1007/978-3-030-01156-7_2