The aim of this paper is to generalize the q-Heisenberg uncertainty principles studied by Bettaibi et al. 2007, to state local uncertainty principles for the q-Fourier-cosine, the q-Fourier-sine, and the q-Bessel-Fourier transforms, then to provide an inequality of Heisenberg-Weyl-type for the q-Bessel-Fourier transform.

We discuss the q deformation of Weyl-Heisenberg algebra in connection with the von Neumann theorem in Quantum Mechanics. We show that the q-deformation parameter labels the Weyl systems in Quantum Mechanics and the unitarily inequivalent representations of the canonical commutation relations in Quantum Field Theory. PACS 02.20.+b; 03.65.Fd; 11.30.Qc;

The paper provides an introduction into p-mechanics, which is a consistent physical theory suitable for a simultaneous description of classical and quantum mechanics. p-Mechanics naturally provides a common ground for several different approaches to quantisation (geometric, Weyl, coherent states, Berezin, deformation, Moyal, etc.) and has a potential for expansions into field and string theorie...

we have applied the method of integration of the heisenberg equation of motion proposed by bender and dunne, and m. kamella and m. razavy to the potential v(q) = v q - µ q with linear and nonlinear dissipation. we concentrate our calculations on the evolution of basis set of weyl ordered operators and calculate the mean position , velocity , the commutation relation [q, p], and the energy of pa...

We show that the series product, which serves as an algebraic rule for connecting state-based input-output systems, is intimately related to the Heisenberg group and the canonical commutation relations. The series product for quantum stochastic models then corresponds to a non-abelian generalization of the Weyl commutation relation. We show that the series product gives the general rule for com...

In this paper we present a survey of the use of differential geometric formalisms to describe Quantum Mechanics. We analyze Schrödinger and Heisenberg frameworks from this perspective and discuss how the momentum map associated to the action of the unitary group on the Hilbert space allows to relate both approaches. We also study Weyl-Wigner approach to Quantum Mechanics and discuss the implica...

We define a three-parameter deformation of the Weyl-Heisenberg algebra that generalizes the q-oscillator algebra. By a purely algebraical procedure, we set up on this quantum space two differential calculi that are shown to be invariant on the same quantum group, extended to a ten-generator Hopf-star-algebra. We prove that, when the values of the parameters are related, the two differential cal...

Abstract In this work, we analyze Gabor frames for the Weyl--Heisenberg group and wavelet extended affine group. Firstly, give necessary sufficient conditions existence of nonstationary translates. Using these conditions, prove from We present a representation functions in closure linear span frame sequence terms Fourier transform window functions. show that canonical dual translates has same s...