Related papers: Algebraic Solution of the Harmonic Oscillator With…

For a q-deformed harmonic oscillator, we find explicit coordinate representations of the creation and annihilation operators, eigenfunctions, and coherent states (the last being defined as eigenstates of the annihilation operator). We…

We carry out a model-theoretic analysis of the Heisenberg algebra. To this end, a geometric structure is associated to the Heisenberg algebra and is shown to be a Zariski geometry. Furthermore, this Zariski geometry is shown to be…

A difference operator realization of quantum deformed oscillator algebra $H_q(1)$ with a Casimir operator freedom is introduced. We show that this $H_q(1)$ have a nonlinear mapping to the deformed quantum su(2) which was introduced by…

Quantum superintegrable systems in two dimensions are obtained from their classical counterparts, the quantum integrals of motion being obtained from the corresponding classical integrals by a symmetrization procedure. For each quantum…

All Lie bialgebra structures on the Heisenberg--Weyl algebra $[A_+,A_-]=M$ are classified and explicitly quantized. The complete list of quantum Heisenberg--Weyl algebras so obtained includes new multiparameter deformations, most of them…

We show that the Euclidean Snyder non-commutative space implies infinitely many different physical predictions. The distinct frameworks are specified by generalized uncertainty relations underlying deformed Heisenberg algebras. Considering…

Using operator ordering techniques based on BCH-like relations of the su(1,1) Lie algebra and a time-splitting approach,we present an alternative method of solving the dynamics of a time-dependent quantum harmonic oscillator for any initial…

The single well 1D harmonic oscillator is one of the most fundamental and commonly solved problems in quantum mechanics. Traditionally, in most introductory quantum mechanics textbooks, it is solved using either a power series method, which…

The symmetry algebra of the two-dimensional anisotropic quantum harmonic oscillator with rational ratio of frequencies, which is characterizing ``pancake'' nuclei, is identified as a non-linear extension of the u(2) algebra. The finite…

We examine a concrete realization of the quantum Weyl algebra and expand it to first order. From here we apply the resulting algebra to a quantum harmonic oscillator in its ground state and observe how a slightly noncommutative space…

Quantum gravity theories predict a minimal length at the order of magnitude of the Planck length, under which the concepts of space and time lose every physical meaning. In quantum mechanics, the insurgence of such minimal length can be…

The symmetry algebra of the N-dimensional anisotropic quantum harmonic oscillator with rational ratios of frequencies is constructed by a method of general applicability to quantum superintegrable systems. The special case of the 3-dim…

This paper investigates a two-dimensional Kemmer oscillator within relativistic quantum mechanics, incorporating minimal length and non-commutative phase space effects. We derive eigen solutions in configuration space $\{p\}$, examining the…

Quantum algebras (also called quantum groups) are deformed versions of the usual Lie algebras, to which they reduce when the deformation parameter q is set equal to unity. From the mathematical point of view they are Hopf algebras. Their…

This lecture consists of two sections. In section 1 we consider the simplest version of a q-deformed Heisenberg algebra as an example of a noncommutative structure. We first derive a calculus entirely based on the algebra and then formulate…

We comment on a recent paper by Chen, Liu, and Ge (J. Phys. A: Math. Gen. 31 (1998) 6473), wherein a nonlinear deformation of su(1,1) involving two deforming functions is realized in the exactly solvable quantum-mechanical problem with P\"…

In two-dimensional noncommutive space for the case of both position - position and momentum - momentum noncommuting, the consistent deformed bosonic algebra at the non-perturbation level described by the deformed annihilation and creation…

We propose a q-deformation of the su(2)-invariant Schrodinger equation of a spinless particle in a central potential, which allows us not only to determine a deformed spectrum and the corresponding eigenstates, as in other approaches, but…

A new approach in solution of simple quantum mechanical problems in deformed space with minimal length is presented. We propose the generalization of Schro\"edinger equation in momentum representation on the case of deformed Heisenberg…

Representations of the quantum q-oscillator algebra are studied with particular attention to local Hamiltonian representations of the Schroedinger type. In contrast to the standard harmonic oscillators such systems exhibit a continuous…