173 research outputs found
Spin Oscillations in Storage Rings
The dependence of the particle rotation frequency on the particle orbit
perturbations is found. The exact equation of spin motion in the cylindrical
coordinate system is derived. The calculated formula for the frequency of g-2
precession is in the best agreement with previous results. Nevertheless, this
formula contains the additional oscillatory term that can be used for fitting.
The influence of spin oscillations on the spin dynamics in the EDM experiment
is negligible.Comment: 5 pages. To appear in the proceedings of 16th International Spin
Physics Symposium (SPIN 2004), Trieste, Italy, 10-16 Oct 200
Classical Limit of Relativistic Quantum Mechanical Equations in the Foldy-Wouthuysen Representation
It is shown that, under the Wentzel-Kramers-Brillouin approximation
conditions, using the Foldy-Wouthuysen representation allows the problem of
finding a classical limit of relativistic quantum mechanical equations to be
reduced to the replacement of operators in the Hamiltonian and quantum
mechanical equations of motion by the respective classical quantities.Comment: 6 page
Foldy-Wouthyusen Transformation and Semiclassical Limit for Relativistic Particles in Strong External Fields
A general method of the Foldy-Wouthyusen (FW) transformation for relativistic
particles of arbitrary spin in strong external fields has been developed. The
use of the found transformation operator is not restricted by any definite
commutation relations between even and odd operators. The final FW Hamiltonian
can be expanded into a power series in the Planck constant which characterizes
the order of magnitude of quantum corrections. Exact expressions for low-order
terms in the Planck constant can be derived. Finding these expressions allows
to perform a simple transition to the semiclassical approximation which defines
a classical limit of the relativistic quantum mechanics. As an example,
interactions of spin-1/2 and scalar particles with a strong electromagnetic
field have been considered. Quantum and semiclassical equations of motion of
particles and their spins have been deduced. Full agreement between quantum and
classical theories has been established.Comment: 10 page
Connection Between Wave Functions in the Dirac and Foldy-Wouthuysen Representations
The connection between wave functions in the Dirac and Foldy-Wouthuysen
representations is found. When the Foldy-Wouthuysen transformation is exact,
upper spinors in two representations differ only by constant factors, and lower
spinors in the Foldy-Wouthuysen representation are equal to zero.Comment: 7 page
- …