Coherent states of non-relativistic electron in the magnetic-solenoid field

In the present work we construct coherent states in the magnetic-solenoid field, which is a superposition of the Aharonov-Bohm field and a collinear uniform magnetic field. In the problem under consideration there are two kinds of coherent states, those which correspond to classical trajectories which embrace the solenoid and those which do not. The constructed coherent states reproduce exactly classical trajectories, maintain their form under the time evolution and form a complete set of functions, which can be useful in semiclassical calculations. In the absence of the solenoid field these states are reduced to the well known in the case of uniform magnetic field Malkin-Man`ko coherent states.

Coherent states of a particle in a magnetic field and the Stieltjes moment problem

A solution to a version of the Stieltjes moment. problem is presented. Using this solution, we construct a family of coherent states of a charged particle in a uniform magnetic field. We prove that these states form an overcomplete set that is normalized and resolves the unity. By the help of these coherent states we construct the Fock-Bergmann representation related to the particle quantization. This quantization procedure takes into account a circle topology of the classical motion. (C) 2009 Elsevier B.V. All rights reserved.

Coherent and semiclassical states in a magnetic field in the presence of the Aharonov-Bohm solenoid

A new approach to constructing coherent states (CS) and semiclassical states (SS) in a magnetic-solenoid field is proposed. The main idea is based on the fact that the AB solenoid breaks the translational symmetry in the xy-plane; this has a topological effect such that there appear two types of trajectories which embrace and do not embrace the solenoid. Due to this fact, one has to construct two different kinds of CS/SS which correspond to such trajectories in the semiclassical limit. Following this idea, we construct CS in two steps, first the instantaneous CS (ICS) and then the time-dependent CS/SS as an evolution of the ICS. The construction is realized for nonrelativistic and relativistic spinning particles both in (2 + 1) and (3 + 1) dimensions and gives a non-trivial example of SS/CS for systems with a nonquadratic Hamiltonian. It is stressed that CS depending on their parameters (quantum numbers) describe both pure quantum and semiclassical states. An analysis is represented that classifies parameters of the CS in such respect. Such a classification is used for the semiclassical decompositions of various physical quantities.

Coherent state quantization of paragrassmann algebras

By using a coherent state quantization of paragrassmann variables, operators are constructed in finite Hilbert spaces. We thus obtain in a straightforward way a matrix representation of the paragrassmann algebra. This algebra of finite matrices realizes a deformed Weyl-Heisenberg algebra. The study of mean values in coherent states of some of these operators leads to interesting conclusions.

Quantization of the damped harmonic oscillator revisited

We return to the description of the damped harmonic oscillator with an assessment of previous works, in particular the Bateman-Caldirola-Kanai model and a new model proposed by one of the authors. We argue the latter has better high energy behavior and is connected to existing open-systems approaches. (C) 2011 Elsevier B.V. All rights reserved.

Pseudoclassical description of scalar particle in non-abelian background and path-integral representations

Path-integral representations for a scalar particle propagator in non-Abelian external backgrounds are derived. To this aim, we generalize the procedure proposed by Gitman and Schvartsman of path-integral construction to any representation of SU(N) given in terms of antisymmetric generators. And for arbitrary representations of SU(N), we present an alternative construction by means of fermionic coherent states. From the path-integral representations we derive pseudoclassical actions for a scalar particle placed in non-Abelian backgrounds. These actions are classically analyzed and then quantized to prove their consistency.

Semiclassical and quantum motions on the non-commutative plane

We study the canonical and the coherent state quantizations of a particle moving in a magnetic field on the non-commutative plane. Using a theta-modified action, we perform the canonical quantization and analyze the gauge dependence of the theory. We compare coherent states quantizations obtained through Malkin-Man`ko states and circular squeezed states. The relation between these states and the ""classical"" trajectories is investigated, and we present numerical explorations of some semiclassical quantities. (C) 2009 Elsevier B.V. All rights reserved.