480 research outputs found
On the Wave Zone of Synchrotron Radiation
The extension of the wave zone of synchrotron radiation is studied.Comment: 6 pages, 1 figur
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
Twisted electron in a strong laser wave
Electrons carrying orbital angular momentum (OAM) have recently been
discovered theoretically and obtained experimentally that opens up
possibilities for using them in high-energy physics. We consider such a twisted
electron moving in external field of a plane electromagnetic wave and study how
this field influences the electron's OAM. Being motivated by the development of
high-power lasers, we focus our attention on a classically strong field regime
for which . It is shown that along with
the well-known "plane-wave" Volkov solution, Dirac equation also has the
"non-plane-wave" solutions, which possess OAM and a spin-orbit coupling, and
generalize the free-electron's Bessel states. Motion of the electron with OAM
in a circularly polarized laser wave reveals a twofold character: the
wave-packet center moves along a classical helical trajectory with some quantum
transverse broadening (due to OAM) existing even for a free electron. Using the
twisted states, we calculate the electron's total angular momentum and predict
its shift in the strong-field regime that is analogous to the well-known shifts
of the electron's momentum and mass (and to a less known shift of its spin) in
intense fields. Since the electron's effective angular momentum is conserved in
a plane wave, as well as in some more general field configurations, we discuss
several possibilities for accelerating non-relativistic twisted electrons by
using the focused and combined electromagnetic fields.Comment: to appear in PR
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
Some Aspects of the Exact Foldy-Wouthuysen Transformation for a Dirac Fermion
The Foldy-Wouthuysen transformation (FWT) is used to separate distinct
components of relativistic spinor field, e.g. electron and positron. Usually,
the FWT is perturbative, but in some cases there is an involution operator and
the transformation can be done exactly. We consider some aspects of an exact
FWT and show that, even if the theory does not admit an involution operator,
one can use the technique of exact FWT to obtain the conventional perturbative
result. Several particular cases can be elaborated as examples
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