Related papers: Perturbative Aspects of q-Deformed Dynamics
We describe some analogues of quantum potentials arising in fractional or deformed Schroedinger equations.
Chaos in classical systems has been studied in plenty over many years. Although the search for chaos in quantum systems has been an area of prominent research over the last few decades, the detailed analysis of many inherently chaotic…
This work addresses the study of the oscillator algebra, defined by four parameters $p$, $q$, $\alpha$, and $\nu$. The time-independent Schr\"{o}dinger equation for the induced deformed harmonic oscillator is solved; explicit analytic…
Some fundamental aspects related with the construction of Robertson-Schr\"odinger like uncertainty principle inequalities are reported in order to provide an overall description of quantumness, separability and nonlocality of quantum…
In this work, we investigate the quantum dynamics of a particle subject to the Morse potential within the framework of Dunkl quantum mechanics. By employing the Dunkl derivative operator, which introduces reflection symmetry, we construct a…
Some physical aspects of $q$-deformed spacetimes are discussed. It is pointed out that, under certain standard assumptions relating deformation and quantization, the classical limit (Poisson bracket description) of the dynamics is bound to…
We consider one dimensional deformed Heisenberg algebra leading to existence of minimal length for coordinate operator and minimal and maximal uncertainty of momentum operator. For this algebra an exactly solvable Hamiltonian is…
Within a self-consistent framework of q-deformed Heisenberg algebra and its equivalent framework of q-deformed boson commutation relations, which relate to the under-cutting phenomenon of Heisenberg's minimal uncertainty relation, special…
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…
The aim of Part II of this paper is to try to describe wave functions on q-deformed versions of position and momentum space. This task is done within the framework developed in Part I of the paper. In order to make Part II self-contained…
The aim of these three papers (I, II, and III) is to develop a q-deformed version of non-relativistic Schroedinger theory. Paper I introduces the fundamental mathematical and physical concepts. The braided line and the three-dimensional…
We construct the integrals of motion for several models of the quantum damped oscillators in nonrelativistic quantum mechanics in a framework of a general approach to the time-dependent Schroedinger equation with variable quadratic…
q-deformed nonlinear field equations are constructed including Klein-Gordon and Maxwell equations. The q-deformation is interpreted as mathematical structure describing specific nonlinearity for which frequency of vibration exponentially…
We discuss, at leading order in $\hbar$, the quantum mechanics of a specific realization in phase space of the Yang model describing noncommutative geometry in a curved background. In particular, we show how the deformation of the…
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…
A geometrical interpretation of Schr\"odinger's kinetic and potential energy operators is proposed, allowing for a covariant momentum space formulation of the dynamics that is relevant for the theories with the deformation of the momentum…
A perturbative formulation of quantum electrodynamics is given in terms of geometrical invariants of the energy-momentum space, whose geometry is taken to be one of a constant curvature. The construction is relevant for different classes of…
The geometric potential in quantum mechanics has been attracted attention recently, providing a formalism to investigate the influence of curvature in the context of low-dimensional systems. In this paper, we study the consequences of a…
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…
In the paper a review of results for recovering of the weak equivalence principle in a space with deformed commutation relations for operators of coordinates and momenta is presented. Different types of deformed algebras leading to a space…