Coherent States and Integrals of the Motion of a Relativistic Charged Particle in an External Field

Bohdan I. Lev, А. А. Семенов, Constantin V. Usenko +1 more

We consider relativistic coherent states for a spin-0 charged particle that satisfy the next additional requirements: (i) the expected values of the standard coordinate and momentum operators are uniquely related to the real and imaginary parts of the coherent state parameter $\ensuremath{\alpha};$ (ii) these states contain only one charge component. Three cases are considered: free particle, relativistic rotator, and particle in a constant homogeneous magnetic field. For the rotational motion of the two latter cases, such a description leads to the appearance of the so-called nonlinear coherent states.

Vladislav G. Bagrov, Иосиф Львович Бухбиндер, Dmitri M Gitman

A. Bermúdez, Miguel Angel Martin-Delgado, E. Solano

We show that a linear superposition of mesoscopic states in relativistic Landau levels can be built when an external magnetic field couples to a relativistic spin 1/2 charged particle. Under suitable initial conditions, the associated Dirac equation produces unitarily superpositions of coherent states involving the particle orbital quanta in a well-defined mesoscopic regime. We demonstrate that these mesoscopic superpositions have a purely relativistic origin and disappear in the nonrelativistic limit.

V. G. Bagrov, Dmitri M Gitman

Quadrupole Fields, Roy J. Glauber

We solve the quantum mechanical problem of the motion of charged particle in a quadrupole field that varies arbitrarily with time. The time-dependent wave functions are shown to be in a simple one-to-one correspondence with the wave functions of an ordinary static-field harmonic oscillator. We define and generate a set of coherent states for the charged particle that provide Gaussian localization about the classical particle trajectories. When the field variation is periodic in time, these minimum uncertainty states are shown to pulsate periodically in size and in phase. Under the action of external fields, coherent states retain their coherence. We discuss the way in which the Kapitza pseudopotential approach approximates the present exact results.

I. M. Ternov, Vladislav G. Bagrov