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We study the elastic scattering of quantum particles based on a real Hilbert space approach to quaternionic quantum mechanics ($\mathbbm H$QM) and derive expression for the wave function, the phase shifts, as well as the optical theorem for…
For certain situations we give a geometrical background for quasiclassical KP calculations based on an explicit connection to quantum mechanics and the collapse of coherent states to coadjoint orbits for classical operators.
Within the Thermal Wave Model framework a comparison among Wigner function, Husimi function, and the phase-space distribution given by a particle tracking code is made for a particle beam travelling through a linear lens with small…
We investigate within the formalism of Symplectic Quantum Mechanics a two-dimensional non-relativistic strong interacting system that represents the bound heavy quark-antiquark state, where it was considered a linear potential in the…
While optics and mechanics are two distinct branches of physics, they are connected. It is well known that geometrical/ray treatment of light has direct analogies to mechanical descriptions of particle motion. However, connections between…
We have treated numerous illustrative examples of spin relaxation problems using Wigner's phase-space formulation of quantum mechanics of particles and spins. The merit of the phase space formalism as applied to spin relaxation problems is…
The correspondence principle in physics between quantum mechanics and classical mechanics suggests deep relations between spectral and geometric entities of Riemannian manifolds. We survey---in a way intended to be accessible to a wide…
Continuous symmetries generated with observables of a quantum theory in the Minkowski spacetime are discussed. An example of an originated in this way algebra of observables is the algebra of observables of the canonical quantum theory,…
Gaussian states are at the heart of quantum mechanics and play an essential role in quantum information processing. In this paper we provide approximation formulas for the expansion of a general Gaussian symbol in terms of elementary…
Quantum mechanical phase space path integrals are re-examined with regard to the physical interpretation of the phase space variables involved. It is demonstrated that the traditional phase space path integral implies a meaning for the…
We determine a positive normalised phase space probability distribution $P$ with minimum mean square fractional deviation from the Wigner distribution $W$ .The minimum deviation, an invariant under phase space rotations, is a quantitative…
The formalism of generalized Wigner transformations developped in a previous paper, is applied to kinetic equations of the Lindblad type for quantum harmonic oscillator models. It is first applied to an oscillator coupled to an equilibrium…
In this thesis we present a direct scheme for measuring quasidistribution functions of light. This scheme, based on photon counting, is derived from a simple relation linking the Wigner function with photon statistics. We develop a full…
In this paper we regard the dynamics obtained from Fermat principle as begin the classical theory of light. We (first-)quantize the action and show how close we can get to the Maxwell theory. We show that Quantum Geometric Optics is not a…
The Wigner distribution function is a quasi-probability distribution. When properly integrated, it provides the correct charge and current densities, but it gives negative probabilities in some points and regions of the phase space.…
The integral of the Wigner function of a quantum mechanical system over a region or its boundary in the classical phase plane, is called a quasiprobability integral. Unlike a true probability integral, its value may lie outside the interval…
We present an operational definition of the Wigner function. Our method relies on the Fresnel transform of measured Rabi oscillations and applies to motional states of trapped atoms as well as to field states in cavities. We illustrate this…
In the framework of the spatial coherence wavelets, different features of the first-order spatial coherence (Young's interference) are analysed by calculating the corresponding marginal power spectrum, a close related quantity to the…
Interactions between charged particles and light occur in real space and time, yet quantum field theory usually describes them in momentum space. Whereas this approach is well suited for calculating emission probabilities and cross…
This paper addresses issues surrounding the concept of fractional quantum mechanics, related to lights propagation in inhomogeneous nonlinear media, specifically restricted to a so called gravitational optics. Besides Schr\"odinger Newton…