Related papers: Deformed harmonic oscillators : coherent states an…
Using deformations inspired by relativistic considerations and phase space symmetry, we deform the position and momentum operators in one dimension. The resulting algebra is shown to yield the q-oscillator algebra in one limiting case and…
The Lie algebra $\mathfrak{su}(1,1)$ can be deformed by a reflection operator, in such a way that the positive discrete series representations of $\mathfrak{su}(1,1)$ can be extended to representations of this deformed algebra…
In this work we make use of deformed operators to construct the coherent states of some nonlinear systems by generalization of two definitions: i) As eigenstates of a deformed annihilation operator and ii) by application of a deformed…
We construct a complete set of eigenfunctions of the q-deformed harmonic oscillator on the quantum line. In particular the eigenfunctions corresponding to the non-Fock part of the spectrum will be constructed.
By factorization of the Hamiltonian describing the quantum mechanics of the continuous q-Hermite polynomial, the creation and annihilation operators of the q-oscillator are obtained. They satisfy a q-oscillator algebra as a consequence of…
We give a method for obtaining states of massive particle representations of the two-parameter deformation of the Poincar\'e algebra proposed in q-alg/9601010, q-alg/9505030 and q-alg/9501026. We discuss four procedures to generate…
Two new types of coherent states associated with the $C_{\lambda}$-extended oscillator, where $C_{\lambda}$ is the cyclic group of order $\lambda$, are introduced. They satisfy a unity resolution relation in the $C_{\lambda}$-extended…
By using a coherent state quantization of paragrassmann variables, operators are constructed in finite Hilbert spaces. We thus obtain in a straightforward way a matrix representation of the paragrassmann algebra. This algebra of finite…
We present a theory of quantized radiation fields described in terms of q-deformed harmonic oscillators. The creation and annihilation operators satisfy deformed commutation relations and the Fock space of states is constructed in this…
Affine transformations (dilatations and translations) are used to define a deformation of one-dimensional $N=2$ supersymmetric quantum mechanics. Resulting physical systems do not have conserved charges and degeneracies in the spectra.…
We analyze systematically several deformations arising from two-dimensional harmonic oscillators which can be described in terms of $\cal{D}$-pseudo bosons. They all give rise to exactly solvable models, described by non self-adjoint…
We consider harmonic maps on simply connected Riemann surfaces into the group $\mathrm{U}(n)$ of unitary matrices of order $n$. It is known that a harmonic map with an associated algebraic extended solution can be deformed into a new…
We consider two-dimensional harmonic oscillator in the complex Bargmann-Fock-Segal representation with $T^*{\mathbb R}^{2}={\mathbb C}^2$ as classical phase space. We show that the eigenfunctions $\psi_n$ of the quantum Hamiltonian…
We construct nonlinear coherent states or f-deformed coherent states for a nonpolynomial nonlinear oscillator which can be considered as placed in the middle between the harmonic oscillator and the isotonic oscillator (Cari\~nena J F et al,…
We study the known coherent states of a quantum harmonic oscillator from the standpoint of the original developed noncommutative integration method for linear partial differential equations. The application of the method is based on the…
Three methods: complexifier, factorization and deformation, for construction of coherent states are presented for one dimensional nonlinear harmonic oscillator (1D NLHO). Since by exploring the Jacobi polynomials $P_n^{a,b}$'s, bridging the…
For the two-parameter $p,q$-deformed Heisenberg algebra introduced recently and in which, instead of usual commutator of $X$ and $P$ in the l.h.s. of basic relation $[X,P] = {\rm i}\hbar$, one uses the $p,q$-commutator, we established…
The aim of this paper is to review our results on description of the multi-parameter deformed oscillators and their oscillator algebras. We define generalized (q;\alpha,\beta,\gamma;\nu)-deformed oscillator algebra and study its irreducible…
Two types of the coherent states for two parameter deformed multimode oscillator system are investigated. Moreover, two parameter deformed $gl(n)$ algebra and deformed symmetric states are constructed.
In this paper, we construct corrections to the raising and lowering (i.e. ladder) operators for a quantum harmonic oscillator subjected to a polynomial type perturbation of any degree and to any order in perturbation theory. We apply our…