Brazilian Journal of Physics
On-line version ISSN 1678-4448
JESUS, V.L.B. de; GUIMARAES, A.P. and OLIVEIRA, I.S.. Classical and quantum mechanics of a charged particle in oscillating electric and magnetic fields. Braz. J. Phys. [online]. 1999, vol.29, n.3, pp. 541-546. ISSN 1678-4448. http://dx.doi.org/10.1590/S0103-97331999000300019.
The motion of a particle with charge q and mass m in a magnetic field given by B = kB0 + B1 [icos(wt) + jsin(wt)] and an electric field which obeys Ñ ´E = -¶B/¶t is analysed classically and quantum-mechanically. The use of a rotating coordinate system allows the analytical derivation of the particle classical trajectory and its laboratory wavefunction. The motion exhibits two resonances, one at w = wc = -qBo/m, the cyclotron frequency, and the other at w = wL = -qBo/2m, the Larmor frequency. For w at the first resonance frequency, the particle acquires a simple closed trajectory, and the effective hamiltonian can be interpreted as that of a particle in a static magnetic field. In the second case a term corresponding to an effective static electric field remains, and the particle orbit is an open line. The particle wave function and eigenenergies are calculated.
Keywords : magnetic resonance; ion trapping; isotope separation; magnetic confinement.