Related papers: Discrete Phase Space: Quantum mechanics and non-si…
A basic theoretical framework is developed in which elementary particles have a component of their wave function extending into higher spatial dimensions. This model postulates an extension of the Schrodinger equation to include a 4th and…
The original Wigner function provides a way of representing in phase space the quantum states of systems with continuous degrees of freedom. Wigner functions have also been developed for discrete quantum systems, one popular version being…
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…
It is the matter of fact that quantum mechanics operates with notions that are not determined in the frame of the mechanics' formalism. Among them we can call the notion of "wave-particle" (that, however, does not appear in both classical…
Three-dimensional quantum electrodynamics exhibits a number of interesting properties, such as dynamical chiral symmetry breaking, weak confinement, and non-Fermi liquid behavior, and also has wide applications in condensed matter physics.…
The quantum mechanical formalism for position and momentum of a particle in a one dimensional cyclic lattice is constructively developed. Some mathematical features characteristic of the finite dimensional Hilbert space are compared with…
The three-dimensional quantum Euclidean space is an example of a non-commutative space that is obtained from Euclidean space by $q$-deformation. Simultaneously, angular momentum is deformed to $so_q(3)$, it acts on the $q$-Euclidean space…
As an example of a noncommutative space we discuss the quantum 3-dimensional Euclidean space $R^3_q$ together with its symmetry structure in great detail. The algebraic structure and the representation theory are clarified and discrete…
It is shown that quantum mechanics on noncommutative (NC) spaces can be obtained by canonical quantization of some underlying constrained systems. Noncommutative geometry arises after taking into account the second class constraints…
We study a one-dimensional singular potential plus three types of regular interactions: constant electric field, harmonic oscillator and infinite square well. We use the Lippman-Schwinger Green function technique in order to search for the…
We report recent progress on the phase space formulation of quantum mechanics with coordinate-momentum variables, focusing more on new theory of (weighted) constraint coordinate-momentum phase space for discrete-variable quantum systems.…
A discrete-time Quantum Walk (QW) is essentially an operator driving the evolution of a single particle on the lattice, through local unitaries. Some QWs admit a continuum limit, leading to familiar PDEs (e.g. the Dirac equation). Recently…
The properties of quantum mechanics with a discrete phase space are studied. The minimum uncertainty states are found, and these states become the Gaussian wave packets in the continuum limit. With a suitably chosen Hamiltonian that gives…
An operator-valued quantum phase space formula is constructed. The phase space formula of Quantum Mechanics provides a natural link between first and second quantization, thus contributing to the understanding of quantization problem. By…
The full spectrum and eigenfunctions of the quantum version of a nonlinear oscillator defined on an N-dimensional space with nonconstant curvature are rigorously found. Since the underlying curved space generates a position-dependent…
A direct numerical simulation of the three-dimensional elektrokinetic instability near a charge selective surface (electric membrane, electrode, or system of micro-/nanochannels) is carried out and analyzed. A special finite-difference…
It is shown by analyzing the $1D$ Schr\"odinger equation that discontinuities in the coupling constant can occur in both the energies and the eigenfunctions. Surprisingly, those discontinuities, which are present in the energies {\it…
A classic no-go theorem in one-dimensional quantum mechanics can be evaded when the potentials are unbounded below, thus allowing for novel parity-paired degenerate energy bound states. We numerically determine the spectrum of one such…
Recently, in Quantum Field theory, there has been an interest in scattering in highly singular potentials. Here, solutions to the stationary Schroedinger equation are presented when the potential is a multiple of an arbitrary positive power…
Quantum mechanical wave functions have phases. These phases either initial or acquired during time evolution usually do not enter the final expressions for observable physical quantities. Nevertheless in many cases the observable physical…