Related papers: Coordinate, Momentum and Dispersion operators in P…
We compute the photon number distribution, the Q distribution function and the wave functions in the momentum and position representation for a single mode squeezed number state using generating functions which allow to obtain any matrix…
The phase point operator $\Delta(q,p)$ is the quantum mechanical counterpart of the classical phase point $(q,p)$. The discrete form of $\Delta(q,p)$ was formulated for an odd number of lattice points by Cohendet et al. and for an even…
We present a detailed discussion of a general theory of phase-space distributions, introduced recently by the authors [J. Phys. A {\bf 31}, L9 (1998)]. This theory provides a unified phase-space formulation of quantum mechanics for physical…
Coherent-state representations are a standard tool to deal with continuous-variable systems, as they allow one to efficiently visualize quantum states in phase space. Here, we work out an alternative basis consisting of monomials on the…
In the paper is presented an invariant quantization procedure of classical mechanics on the phase space over flat configuration space. Then, the passage to an operator representation of quantum mechanics in a Hilbert space over…
Commuting and noncommuting space-time coordinates in a class of deformed special relativity theories are investigated. Their momentum space representation, transformation behaviour, space-time algebra, invariants and the corresponding field…
It is known that local operators in quantum field theory transform in representations of ordinary global symmetry groups. The purpose of this paper is to generalise this statement to extended operators such as line and surface defects. We…
Motivated by the sharp contrast between classical and quantum physics as probability theories, in these lecture notes I introduce the basic notions of operator algebras that are relevant for the algebraic approach to quantum physics.…
A combined method for analyzing quantum dynamical equations which uses the Bohmian mechanics and the quantum phase space representation is proposed. It is based on a presentation of the wave function in phase space in a polar form. The…
INTRODUCTION This papers deals with partial differential equations of second order, linear, with constant and not constant coefficients, in two variables, which admit real characteristics. I face the study of PDEs with the mentality of the…
We propose a variational wave function to represent quantum skyrmions as bosonic operators. The operator faithfully reproduces two fundamental features of quantum skyrmions: their classical magnetic order and a "quantum cloud" of local…
One of the key conceptual challenges in quantum gravity is to understand how quantum theory should modify the very notion of spacetime. One way to investigate this question is to study the alternatives to Schr\"odinger quantum mechanics.…
A possibility to use an integral operator for establishing the link between physical and structural levels of materials in modeling diffusion processes is considered. We show how to perform the transition from the stochastic description of…
We present in the article the formulation of a version of Lorentz covariant quantum mechanics based on a group theoretical construction from a Heisenberg-Weyl symmetry with position and momentum operators transforming as Minkowski…
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 effects of a beamsplitter are frequently described mathematically as a matrix acting on a two input ports vector. This might be comprehensive for a scalar field but certainly insufficient in case of photons which are vector fields. In…
The position operator (defined within the Schroedinger representation in the standard way) becomes meaningless when periodic boundary conditions are adopted for the wavefunction, as usual in condensed matter physics. We show how to define…
This paper gives a representation of the most general positive operator valued measure in Minkowski space-time, covariant with respect to the Poincare' group. It provides the correct mathematical description of the space-time coordinates of…
Dissipaton-equation-of-motion (DEOM) theory [Y. J. Yan, J. Chem. Phys. 140, 054105 (2014)] is an exact and nonperturbative many-particle method for open quantum systems. The existing dissipaton algebra treats also the dynamics of hybrid…
Of crucial importance to the development of quantum computing and information has been the construction of a quantum operations formalism that admits a description of quantum noise while simultaneously revealing the behavior of an open…