Related papers: Quantum Mechanical Properties of Bessel Beams
Quantum optics experiments on "bright" beams typically probe correlations between side-band modes. However the extra degree of freedom represented by this dual mode picture is generally ignored. We demonstrate the experimental operation of…
We study the commutation relations, uncertainty relations and spectra of position and momentum operators within the framework of quantum group % symmetric Heisenberg algebras and their (Bargmann-) Fock representations. As an effect of the…
Light carrying orbital angular momentum (OAM)--known as vortex beams--has broadened the scope of understanding and applications of light's angular momentum. Optical tweezers using OAM, often referred to as optical spanners, have…
We present generalized expressions to calculate the orbital angular momentum for invariant beams using scalars potentials. The solutions can be separated into transversal electric TE, transversal magnetic TM and transversal electromagnetic…
Binary operations on algebras of observables are studied in the quantum as well as in the classical case. It is shown that certain natural compatibility conditions with the associative product imply the properties which usually are…
Quantum estimation of the operators of a system is investigated by analyzing its Liouville space of operators. In this way it is possible to easily derive some general characterization for the sets of observables (i.e. the possible quorums)…
In analogy with conventional quantum mechanics, non-commutative quantum mechanics is formulated as a quantum system on the Hilbert space of Hilbert-Schmidt operators acting on non-commutative configuration space. It is argued that the…
Relations and isomorphisms between quantum field theories in operator and functional integral formalisms are analyzed from the viewpoint of inequivalent representations of commutator or anticommutator rings of field operators. A functional…
A subclass of dynamical semigroups induced by the interaction of a quantum system with an environment is introduced. Such semigroups lead to the selection of a stable subalgebra of effective observables. The structure of this subalgebra is…
We point out a possible complementation of the basic equations of quantum mechanics in the presence of gravity. This complementation is suggested by the well-known fact that quantum mechanics can be equivalently formulated in the position…
The coherent manipulation of the atomic matter waves is of great interest both in science and technology. In order to study how an atom optic device alters the coherence of an atomic beam, we consider the quantum lens proposed by Averbukh…
The interpretation of optical spectra requires thorough comprehension of quantum mechanics, especially understanding the concept of angular momentum operators. Suppose now that a transformation from laboratory-fixed to molecule-attached…
We consider the quantum mechanics of a particle on a noncommutative two-sphere with the coordinates obeying an SU(2)-algebra. The momentum operator can be constructed in terms of an $SU(2)\times SU(2)$-extension and the Heisenberg algebra…
An explicit formula for a new type of beams, which in this work are called the "special" hyperbolic Bessel-Gaussian (SHBG) beams, has been derived, using the method of the Hankel transform formulated in our previous work. The fundamental…
Relations between Hamiltonian mechanics and quantum mechanics are studied. It is stressed that classical mechanics possesses all the specific features of quantum theory: operators, complex variables, probabilities (in case of ergodic…
We give a review of concepts related to connection of classical and quantum theories, from the phase space perspective. Quantum theory is described by non-commutative operators of coordinates and momenta, results in values having a certain…
We study the notion of molecules in coorbit spaces. The main result states that if an operator, originally defined on an appropriate space of test functions, maps atoms to molecules, then it can be extended to a bounded operator on coorbit…
The motion of neutral, polarizable atoms (also called neutral particles in this work) in the field of the Bessel beam is considered. It is shown in the numerical way, that the Bessel rings, i.e., the regions of high energy concentration can…
We formulate quantum mechanics in spacetimes with real-order fractional geometry and more general factorizable measures. In spacetimes where coordinates and momenta span the whole real line, Heisenberg's principle is proven and the…
In Quantum Physics, a measurement is represented by a projection on some closed subspace of a Hilbert space. We study algebras of operators that abstract from the algebra of projections on closed subspaces of a Hilbert space. The properties…