Related papers: Properties of Phase Space Wavefunctions and Eigenv…
The aim of this paper is to present a study on the representations of coordinate, momentum and dispersion operators in the framework of a phase space representation of quantum mechanics that we have introduced and studied in previous works.…
A study on a method for the establishment of a phase space representation of quantum theory is presented. The approach utilizes the properties of Gaussian distribution, the properties of Hermite polynomials, Fourier analysis and the current…
The time periodic circuit theory is exploited to introduce an appropriate translation operator that is invariant under the change of the spatial unit cell. Useful properties of the operator are derived. By casting the problem in an…
We introduce new representations to formulate quantum mechanics on noncommutative phase space, in which both coordinate-coordinate and momentum-momentum are noncommutative. These representations explicitly display entanglement properties…
In this work, we introduce a new difference equation which is discrete analogue of Diffusion differential equation and analyze some essential spectral properties, Diffusion difference operator is self-adjoint, eigenvalues of this problem…
Quantizing the transfer of energy and momentum between interacting particles, we obtain a quantum impulse equation and relations that the corresponding mechanical power, force and torque satisfy. In addition to the energy-frequency and…
Employing the phase-space representation of second order ordinary differential equations we developed a method to find the eigenvalues and eigenfunctions of the 1-dimensional time independent Schr\"odinger equation for quantum model…
The Wigner eigenfunctions of a free quantum particle propagating on a plane are derived. Two possibilities are analysed. Firstly, the particle of given energy and angular momentum is discussed. In that case, a special choice of coordinates…
In this paper, we consider the operator properties of various phononic eigenvalue problems. We aim to answer some fundamental questions about the eigenvalues and eigenvectors of phononic operators. These include questions about the…
A quantum mechanics representation based on position ($\vec{r}$), linear momentum($\vec{p}$) and energy($E$) eigenvalues is presented here. A set of equations, explicitly independent on wave function, was derived relating these observables.…
Dynamical systems associated with a q-deformed two dimensional phase space are studied as effective dynamical systems described by ordinary variables. In quantum theory, the momentum operator in such a deformed phase space becomes a…
We explore the manipulation in phase space of many-body wavefunctions that exhibit self-similar dynamics, under the application of sudden force and/or in the presence of a constant acceleration field. For this purpose, we work out a common…
In quantum mechanics, the operator representing the displacement of a system in position or momentum is always accompanied by a path-dependent phase factor. In particular, two non-parallel displacements in phase space do not compose…
We estimate the distribution of the eigenvalues of a family of time-frequency localization operators whose eigenfunctions are the well-known Prolate Spheroidal Wave Functions from mathematical physics. These operators are fundamental to the…
A diffusion process for charge distributions in a phase space is examined. The corresponding charge moves in a force field and under an action of a random field. There are the diffusion motions for coordinates and for momenta. In our model,…
We examine the procedure to construct the variables of use for the momentum representation in quantum mechanics. The momentum variables must be chosen properly conjugate to the corresponding position space variables, such that valid…
Based on the novel prescription for the power of a complex number, a new expression for the eigenfunction of the operator of the third component of the angular momentum is presented. These functions are normalizable, single valued and are…
In quantum mechanics, spatial wavefunctions describe distributions of a particle's position or momentum, but not of angular momentum $j$. In contrast, here we show that a spatial wavefunction, $j_m (\phi,\theta,\chi)=~e^{i m \phi} \delta…
The paper considers the general form of self-adjoint boundary value problems for momentum operators with nonlocal potentials. We give an analysis of the eigenvalue distribution as zeros of the characteristic functions, for which their…
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…