The manipulation problem in quantum mechanics

Abstract

We explain the meaning of dynamical manipulation, and we illustrate its mechanism by using a system composed of a charged particle in a Penning trap. It is shown that by means of appropriate electric shocks (delta-like pulses) applied to the trap walls one can induce the squeezing transformation. The geometric phases associated to some cyclic evolutions, induced either by the standard fields of the Penning trap or by the superposition of these plus a rotating magnetic field, are analysed

15 pages, latex, 5 Postscript figures, uses epsf, to appear in the proceedings of the workshop `Symmetries in quantum mechanics and quantum optics', Burgos (Spain), september 21-24, 1998