相关论文: Bargmann representations for deformed harmonic osc…
We show that three deformation functors (deformations of the product, flat deformations and deformations of the relations) assigned to an associative algebra are naturally isomorphic.
q-oscillators are associated to the simplest non-commutative example of Hopf algebra and may be considered to be the basic building blocks for the symmetry algebras of completely integrable theories. They may also be interpreted as a…
We construct the systems of the harmonic and Pais-Uhlenbeck oscillators, which are invariant with respect to arbitrary noncompact Lie algebras. The equations of motion of these systems can be obtained with the help of the formalism of…
We analyze the two-mode squeezed harmonic oscillator and the $k$th-order harmonic generation within the framework of Bargmann-Hilbert spaces of entire functions. For the displaced, single-mode squeezed and two-mode squeezed harmonic…
The fundamental properties of biquaternions (complexified quaternions) are presented including several different representations, some of them new, and definitions of fundamental operations such as the scalar and vector parts, conjugates,…
The spectral measure of the position (momentum) operator $X$ for $q$-deformed oscillator is calculated in the case of the indetermine Hamburger moment problem. The exposition is given for concrete choice of generators for $q$-oscillator…
We construct a generalised expression for the normal ordering of (a+a^{\dagger})^{m} for integral values of m and use the result to study the quantum anharmonic oscillator problem in the Heisenberg approach. In particular, we derive…
The operator algebras of a new family of relativistic geometric models of the relativistic oscillator are studied. It is shown that, generally, the operator of number of quanta and the pair of the shift operators of each model are the…
This paper is a natural continuation of the previous paper J.Phys. A: Math.Theor. 44 (2011) 425204, arXiv 0907.1736 [quant-ph] where oscillator representations for nonnegative Calogero Hamiltonians with coupling constant $\alpha\geq-1/4$…
In this investigation, the displacement operator is revisited. We established a connection between the Hermitian version of this operator with the well-known Weyl ordering. Besides, we characterized the quantum properties of a simple…
Nambu's construction of multi-linear brackets for super-integrable systems can be thought of as degenerate Poisson brackets with a maximal set of Casimirs in their kernel. By introducing privileged coordinates in phase space these…
Concerning the energy of harmonic oscillator, a prescription is proposed for making the original form unchanged even after q-deformation. Applicability of the prescription is limited, but, it can be applied to various cases which are well…
A unified method of calculating structure functions from commutation relations of deformed single-mode oscillator algebras is presented. A natural approach to building coherent states associated to deformed algebras is then deduced.
We analyze the spectrum and normal mode representation of general quadratic bosonic forms $H$ not necessarily hermitian. It is shown that in the one-dimensional case such forms exhibit either an harmonic regime where both $H$ and…
Let~$X=\Po/\Gamma$ be an~$n$-punctured sphere, $n>3$. We introduce and study~$n-3$ deformation operators on the space of modular forms~$M_*(\Gamma)$ based on the classical theory of uniformizing differential equations and accessory…
We define a q-deformation of the Dirac operator, inspired by the one dimensional q-derivative. This implies a q-deformation of the partial derivatives. By taking the square of this Dirac operator we find a q-deformation of the Laplace…
A deformation of the harmonic oscillator algebra associated with the Morse potential and the SU(2) algebra is derived using the quantum analogue of the anharmonic oscillator. We use the quantum oscillator algebra or $q$-boson algebra which…
Starting from generalized position operators, we derive complex and quaternionic angular momentum operators along with their commutation algebra as well. These algebras differ from the standard Hermitian ones, especially in terms of…
A deformation of Heisenberg algebra induces among other consequences a loss of Hermiticity of some operators that generate this algebra. Therefore, these operators are not Hermitian, nor is the Hamiltonian operator built from them. In the…
For the $q$-deformed canonical commutation relations $a(f)a^\dagger(g) = (1-q)\,\langle f,g\rangle{\bf1}+q\,a^\dagger(g)a(f)$ for $f,g$ in some Hilbert space ${\cal H}$ we consider representations generated from a vector $\Omega$ satisfying…