Completeness for coherent states in a magnetic–solenoid field

Vladislav G. Bagrov, Sergei P. Gavrilov, K. Górska +1 more

Damião Pedro Meira Filho

Vladislav G. Bagrov, Sergei P. Gavrilov, Dmitri M Gitman +1 more

This article completes our study of coherent states in the so-called magnetic-solenoid field (a colinear combination of a constant uniform magnetic field and Aharonov-Bohm solenoid field) presented in JPA 2010 and 2011. Here we succeeded to prove nontrivial completeness relations for non-relativistic and relativistic coherent states in such a field. In addition, we solve here the relevant Stieltjes moment problem and present a comparative analysis of our coherent states and the well-known in the case of pure uniform magnetic field Malkin-Man'ko coherent states.

Vladislav G. Bagrov, Sergei P. Gavrilov, Dmitri M Gitman +1 more

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.

V. V. Dodonov

I.A. Malkin, Vladimir I. Man’ko, D. A. Trifonov