Related papers: Coordinate, Momentum and Dispersion operators in P…
In this paper, we define the general framework to describe the diffusion operators associated to a positive matrix. We define the equations associated to diffusion operators and present some general properties of their state vectors. We…
We present a phase space formulation of quantum mechanics in the Schr\"odinger representation and derive the associated Weyl pseudo-differential calculus. We prove that the resulting theory is unitarily equivalent to the standard…
The role of response operators is well established in quantum mechanics. We investigate their use for universal quantum machine learning models of response properties in molecules. After introducing a theoretical basis, we present and…
Explicit expressions for most interesting quantum operators in optical tomography representation are found. General formalism of symbols of operators is presented in optical tomographic representation. The symbols of the operators are found…
The problem of defining time (or phase) operator for three-dimensional harmonic oscillator has been analyzed. A new formula for this operator has been derived. The results have been used to demonstrate a possibility of representing…
The one-particle momentum transfer operator is derived in point-form spectator approximation for $NN$ system. General expression is applied to elastic electron-deuteron scattering and to deuteron photodisintegration.
In quantum mechanics textbooks the momentum operator is defined in the Cartesian coordinates and rarely the form of the momentum operator in spherical polar coordinates is discussed. Consequently one always generalizes the Cartesian…
In momentum space the Feynman propagator $D_{F}(k)$ at non-zero temperature is defined by a simple dispersion relation with the familiar property of being an even function of $k^{0}$ and analytic for Re$(k^{0})^{2}>0$. The coordinate space…
It is shown that an operator can be defined in the abstract space of random matrices ensembles whose matrix elements statistical distribution simulates the behavior of the distribution found in real physical systems. It is found that the…
Nonlinear dynamical systems are ubiquitous in science and engineering, yet analysis and prediction of these systems remains a challenge. Koopman operator theory circumvents some of these issues by considering the dynamics in the space of…
It is shown that the the quantum phase space distributions corresponding to a density operator $\rho$ can be expressed, in thermofield dynamics, as overlaps between the state $\mid \rho >$ and "thermal" coherent states. The usefulness of…
Angular momentum is important concept in physics, and its phase space properties are important in various applications. In this work phase space analysis of the angular momentum is made from its classical definition, and by imposing…
We discuss the Kirkwood-Rihaczek phase space distribution and analyze a whole new class of quasi-distributions connected with this function. All these functions have the correct marginals. We construct a coherent state representation of…
Introducing asymmetry into the Weyl representation of operators leads to a variety of phase space representations and new symbols. Specific generalizations of the Husimi and the Glauber-Sudarshan symbols are explicitly derived
Generators of the Poincar\'e group, for a free massive scalar field, are usually expressed in the momentum space. In this work we perform a transformation of these generators into the coordinate space. This (spatial)-position space is…
Interferences in the distributions of complementary variables for angular momentum - two level systems are discussed. A quantum phase distribution is introduced for angular momentum. Explicit results for the phase distributions and the…
We consider a family {P} of determinantal point processes arising in representation theory and random matrix theory. The processes live on the one-dimensional lattice and their correlation kernels correspond to projection operators in the…
We study the representations of the three-dimensional Euclidean Snyder-de Sitter algebra. This algebra generates the symmetries of a model admitting two fundamental scales (Planck mass and cosmological constant) and is invariant under the…
We continue to derive spacetime quantities and spin 1/2 propagators from rotations. Rotation-invariant projection operators are found for each element of a four element basis, i.e. a basis for four component quantities with specific…
We consider a general schema involving measure spaces, contractions and linear and continuous operators. Within the framework of this schema we use our sesquilinear uniform integral and introduce some integral operators on continuous vector…