Related papers: ${\cal D}$-deformed harmonic oscillators
We introduce the Dunkl-Darboux III oscillator Hamiltonian in N dimensions, defined as a $\lambda-$deformation of the N-dimensional Dunkl oscillator. This deformation can be interpreted either as the introduction of a non-constant curvature…
The two dimensional set of canonical relations giving rise to minimal uncertainties previously constructed from a q-deformed oscillator algebra is further investigated. We provide a representation for this algebra in terms of a flat…
An unusual type of the exact solvability is reported. It is exemplified by the Coulomb plus harmonic oscillator in D dimensions after a complexification of its Hamiltonian which keeps the energies real. Infinitely many bound states are…
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…
This work addresses a ${\theta}(\hat{x},\hat{p})-$deformation of the harmonic oscillator in a $2D-$phase space. Specifically, it concerns a quantum mechanics of the harmonic oscillator based on a noncanonical commutation relation depending…
The concept of quasi-bosons or composite bosons (like mesons, excitons etc.) has a wide range of potential physical applications. Even composed of two pure fermions, the quasi-boson creation and annihilation operators satisfy non-standard…
A general method based on the polynomial deformations of the Lie algebra sl(2,R) is proposed in order to exhibit the quasi-exactly solvability of specific Hamiltonians implied by quantum physical models. This method using the…
We systematically study inhomogeneous Hamiltonians in two-dimensional conformal field theories within the framework of the AdS/CFT correspondence by relating them to two-dimensional curved backgrounds. We propose a classification of…
We consider quantum models corresponding to superymmetrizations of the two-dimensional harmonic oscillator based on worldline $d=1$ realizations of the supergroup SU$(\,{\cal N}/2\,|1)$, where the number of supersymmetries ${\cal N}$ is…
A deformed boson mapping of the Marumori type is derived for an underlying $su(2)$ algebra. As an example, we bosonize a pairing hamiltonian in a two level space, for which an exact treatment is possible. Comparisons are then made between…
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 briefly review some recent results concerning algebraical (oscillator) aspects of the $N$-body single-species and multispecies Calogero models in one dimension. We show how these models emerge from the matrix generalization of the…
Harmonic oscillator in noncommutative two dimensional lattice are investigated. Using the properties of non-differential calculus and its applications to quantum mechanics, we provide the eigenvalues and eigenfunctions of the corresponding…
Using as a prototype example the harmonic oscillator we show how losing self-adjointness of the hamiltonian $H$ changes drastically the related functional structure. In particular, we show that even a small deviation from strict…
Two new families of completely integrable perturbations of the N-dimensional isotropic harmonic oscillator Hamiltonian are presented. Such perturbations depend on arbitrary functions and N free parameters and their integrals of motion are…
A similarity transformation is constructed through which a system of particles interacting with inverse-square two-body and harmonic potentials in one dimension, can be mapped identically, to a set of free harmonic oscillators. This…
Harmonic oscillator, in 2-dimensional noncommutative phase space with non-vanishing momentum-momentum commutators, is studied using an algebraic approach. The corresponding eigenvalue problem is solved and discussed.
We obtain the eigenvalues of the harmonic oscillator in a space with a screw dislocation. By means of a suitable nonorthogonal basis set with variational parameters we obtain sufficiently accurate eigenvalues for an arbitrary range of…
We find that, in presence of the Snyder geometry, the quantization of d isotropic harmonic oscillators can be solved exactly.
The q-deformed harmonic oscillator is studied in the light of q-deformed phase space variables. This allows a formulation of the corresponding Hamiltonian in terms of the ordinary canonical variables $x$ and $p$. The spectrum shows…