New solutions of relativistic wave equations in magnetic fields and longitudinal fields

We demonstrate how one can describe explicitly the present arbitrariness in solutions of relativistic wave equations in external electromagnetic fields of special form. This arbitrariness is connected to the existence of a transformation, which reduces effectively the number of variables in the initial equations. Then we use the corresponding representations to construct new sets of exact solutions, which may have a physical interest. Namely, we present new sets of stationary and nonstationary solutions in magnetic field and in some superpositions of electric and magnetic fields.Comment: 25 pages, LaTex fil

Quantum motion in superposition of Aharonov-Bohm with some additional electromagnetic fields

The structure of additional electromagnetic fields to the Aharonov-Bohm field, for which the Schr\"odinger, Klein-Gordon, and Dirac equations can be solved exactly are described and the corresponding exact solutions are found. It is demonstrated that aside from the known cases (a constant and uniform magnetic field that is parallel to the Aharonov-Bohm solenoid, a static spherically symmetrical electric field, and the field of a magnetic monopole), there are broad classes of additional fields. Among these new additional fields we have physically interesting electric fields acting during a finite time, or localized in a restricted region of space. There are additional time-dependent uniform and isotropic electric fields that allow exact solutions of the Schrodinger equation. In the relativistic case there are additional electric fields propagating along the Aharonov-Bohm solenoid with arbitrary electric pulse shape

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

A new approach to constructing coherent states (CS) and semiclassical states (SS) in 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 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.Comment: 35 pages, 2 figures. Some typos in (77), (101), and (135) corrected with respect to the published version. Results unchange

Effective spectrum width of the synchrotron radiation

For an exact quantitative description of spectral properties of synchrotron radiation (SR), the concept of effective width of the spectrum is introduced. In the most interesting case, which corresponds to the ultrarelativistic limit of SR, the effective width of the spectrum is calculated for the polarization components, and new physically important quantitative information on the structure of spectral distributions is obtained. For the first time, the spectral distribution for the circular polarization component of the SR for the upper half-space is obtained within classical theory

Dependence of effective spectrum width of synchrotron radiation on particle energy

For an exact quantitative description of spectral properties in the theory of synchrotron radiation, the concept of effective spectral width is introduced. In the classical theory, numeric calculations of effective spectral width (using an effective width not exceeding 100 harmonics) for polarization components of synchrotron radiation are carried out. The dependence of the effective spectral width and initial harmonic on the energy of a radiating particle is established

Aspects of Two-Level Systems under External Time Dependent Fields

The dynamics of two-level systems in time-dependent backgrounds is under consideration. We present some new exact solutions in special backgrounds decaying in time. On the other hand, following ideas of Feynman, Vernon and Hellwarth, we discuss in detail the possibility to reduce the quantum dynamics to a classical Hamiltonian system. This, in particular, opens the possibility to directly apply powerful methods of classical mechanics (e.g. KAM methods) to study the quantum system. Following such an approach, we draw conclusions of relevance for ``quantum chaos'' when the external background is periodic or quasi-periodic in time.Comment: To appear in J. Phys. A. Mathematical and Genera

Charged particles in crossed and longitudinal electromagnetic fields and beam guides

We consider a class of electromagnetic fields that contains crossed fields combined with longitudinal electric and magnetic fields. We study the motion of a classical particle (solutions of the Lorentz equations) in such fields. Then, we present an analysis that allows one to decide which fields from the class act as a beam guide for charged particles, and we find some time-independent and time-dependent configurations with beam guiding properties. We demonstrate that the Klein-Gordon and Dirac equations with all the fields from the class can be solved exactly. We study these solutions, which were not known before, and prove that they form complete and orthogonal sets of functions.Comment: 14 page