相关论文: A class of weak pseudo-bosons and their bi-coheren…
We consider the Hamiltonian $H$ of a particle in one dimension with a position dependent mass for which we apply the recent strategy of the so-called {\em abstract ladder operators}, in the attempt to find its eigenvalues and eigenvectors.…
Ladder operators are useful, if not essential, in the analysis of some given physical system since they can be used to find easily eigenvalues and eigenvectors of its Hamiltonian. In this paper we extend our previous results on abstract…
We show how the notion of {\em pseudo-bosons}, originally introduced as operators acting on some Hilbert space, can be extended to a distributional settings. In doing so, we are able to construct a rather general framework to deal with…
In this paper we consider squares of pseudo-bosonic ladder operators and we use them to produce explicit examples of eigenstates of certain operators satisfying a deformed $\mathfrak{su}(1,1)$ Lie algebra. We show how these eigenstates may,…
In this paper we continue our analysis on deformed canonical commutation relations and on their related pseudo-bosons and bi-coherent states. In particular, we show how to extend the original approach outside the Hilbert space…
We show how the one-mode pseudo-bosonic ladder operators provide concrete examples of nilpotent Lie algebras of dimension five. It is the first time that an algebraic-geometric structure of this kind is observed in the context of…
Using the {\it nonlinear coherent states method}, a formalism for the construction of the coherent states associated to {\it "inverse bosonic operators"} and their dual family has been proposed. Generalizing the approach, the "inverse of…
Coherent states (CS) for non-Hermitian systems are introduced as eigenstates of pseudo-Hermitian boson annihilation operators. The set of these CS includes two subsets which form bi-normalized and bi-overcomplete system of states. The…
We introduce an extended version of the Swanson model, defined on a two-dimensional non commutative space, which can be diagonalized exactly by making use of pseudo-bosonic operators. Its eigenvalues are explicitly computed and the…
Extending our previous analysis on bi-coherent states, we introduce here a new class of quantum mechanical vectors, the \emph{bi-squeezed states}, and we deduce their main mathematical properties. We relate bi-squeezed states to the…
We consider a fully pseudo-bosonic Swanson model and we show how its Hamiltonian $H$ can be diagonalized. We also deduce the eigensystem of $H^\dagger$, using the general framework and results deduced in the context of pseudo-bosons. We…
In a recent paper a pair of operators $a$ and $b$ satisfying the equations $a^\dagger a=bb^\dagger+\gamma\1$ and $aa^\dagger=b^\dagger b+\delta\1$, has been considered, and their nature of ladder operators has been deduced and analysed.…
We propose a deformed version of the generalized Heisenberg algebra by using techniques borrowed from the theory of pseudo-bosons. In particular, this analysis is relevant when non self-adjoint Hamiltonians are needed to describe a given…
We inquire into some properties of diagonalizable pseudo-Hermitian operators, showing that their definition can be relaxed and that the pseudo-Hermiticity property is strictly connected with the existence of an antilinear symmetry. This…
In a series of recent papers one of us has analyzed in some details a class of elementary excitations called {\em pseudo-bosons}. They arise from a special deformation of the canonical commutation relation $[a,a^\dagger]=\1$, which is…
After a brief review on $\D$-pseudo-bosons we introduce what we call {\em Riesz bi-coherent states}, which are pairs of states sharing with ordinary coherent states most of their features. In particular, they produce a resolution of the…
Previous $\lambda$-deformed {\it non-Hermitian} Hamiltonians with respect to the usual scalar product of Hilbert spaces dealing with harmonic oscillator-like developments are (re)considered with respect to a new scalar product in order to…
The increasingly popular concept of a hidden Hermiticity of operators (i.e., of their Hermiticity with respect to an {\it ad hoc} inner product in Hilbert space) is compared with the recently introduced notion of {\em non-linear…
We demonstrate that a non self-adjoint Hamiltonian of harmonic oscillator type defined on a two-dimensional noncommutative space can be diagonalized exactly by making use of pseudo-bosonic operators. The model admits an antilinear symmetry…
We build the coherent states for a family of solvable singular Schr\"odinger Hamiltonians obtained through supersymmetric quantum mechanics from the truncated oscillator. The main feature of such systems is the fact that their…