Related papers: Coherent states for the q-deformed quantum mechani…
We review some aspects of the relation between ordinary coherent states and q-deformed generalized coherent states with some of the simplest cases of quantum Lie algebras. In particular, new properties of (q-)coherent states are utilized to…
The uncertainty relations for the position and momentum of a quantum particle on a circle are identified minimized by the corresponding coherent states. The sqeezed states in the case of the circular motion are introduced and discussed in…
The coherent states for the quantum mechanics on a torus and their basic properties are discussed.
The coherent states for a particle on a sphere are introduced. These states are labelled by points of the classical phase space, that is the position on the sphere and the angular momentum of a particle. As with the coherent states for a…
The coherent states for the quantum particle on the circle are introduced. The Bargmann representation within the actual treatment provides the representation of the algebra $[\hat J,U]=U$, where $U$ is unitary, which is a direct…
The von Neumann type subsystems of $q$-deformed coherent states are considered. The completeness of such subsystems is proved.
We compare the geometrical and physical properties of the maths-type coherent states for $q>1$ with those of the same for $0 < q < 1$.
We describe a $q$-deformed dynamical system corresponding to the quantum free particle moving along the circle. The algebra of observables is constructed and discussed. We construct and classify irreducible representations of the system.
Examples are given of q-deformed systems that may be interpreted by the standard rules of quantum theory in terms of new degrees of freedom and supplementary quantum numbers.
With a q-deformed quantum mechanical framework, features of the uncertainty relation and a novel formulation of the Schr\"odinger equation are considered.
Maths-type q-deformed coherent states with $q > 1$ allow a resolution of unity in the form of an ordinary integral. They are sub-Poissonian and squeezed. They may be associated with a harmonic oscillator with minimal uncertainties in both…
In this paper, the generalized coherent state for quantum systems with degenerate spectra is introduced. Then, the nonclassicality features and number-phase entropic uncertainty relation of two particular degenerate quantum systems are…
The coherent states for twist-deformed oscillator model provided in article [1] are constructed. Besides, it is demonstrated that the energy spectrum of considered model is labeled by two quantum numbers - by so-called main and azimutal…
The coherent states are constructed for a charged particle in a uniform magnetic field based on coherent states for the circular motion which have recently been introduced by the authors.
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…
Coherent states on the quantum group $SU_q(2)$ are defined by using harmonic analysis and representation theory of the algebra of functions on the quantum group. Semiclassical limit $q\rightarrow 1$ is discussed and the crucial role of…
A new kind of deformed calculus (the D-deformed calculus) that takes place in fractional-dimensional spaces is presented. The D-deformed calculus is shown to be an appropriate tool for treating fractional-dimensional systems in a simple way…
p-Mechanics is a consistent physical theory which describes both quantum and classical mechanics simultaneously. We continue the development of p-mechanics by introducing the concept of states. The set of coherent states we introduce allow…
We provide a unified approach for finding the coherent states of various deformed algebras, including quadratic, Higgs and q-deformed algebras, which are relevant for many physical problems. For the non-compact cases, coherent states, which…
We have analyzed theoretically the operation of the Bayesian quantum feedback of a solid-state qubit, designed to maintain perfect coherent oscillations in the qubit for arbitrarily long time. In particular, we have studied the feedback…