Quantum And Classical Dynamical Behaviors Of Few-Body Coulomb Systems In External Fields

The atomic, molecular, and ionic few-body Coulomb systems in external fields are extremely hot topics in modern physics. In the past century the behaviors of charged-particle systems in an external field have been the subjects of extensive and intensive studies. The invention of the ionic trap in the 1950s ushered the experimental study of the dynamical behaviors of few-body Coulomb systems into a new era. In later studies investigators have taken advantage of new technology like the Paul trap and Penning trap to study these behaviors. This allowed the experimental characterization of the basic properties of the atomic and molecular systems in external fields. The application of laser cooling technology to the ionic trap in the last ten years not only has provided even more solid experimental basis to generate new materials, observe new phenomena, and gain new knowledge, but also has opened some new research areas like quantum information and quantum computation. As a result of the improvement of experimental extensive laser technology, the problems of dissociation and ionization of Coulomb systems have now become a very important topic in the extensive field physics and chemical physics. Recent studies on the dissociation of the hydrogen molecular ion revealed some interesting and unique properties of its dissociating procedure. The time-dependent Schrodinger equation of this procedure, however, remains an unsolved problem. So far there has been very little classical treatment of this problem.The Coulomb systems in an external field are usually classified by the behaviors of charged particles. The hetero-charged system contains particles of different mass and charge, such as atomic hydrogen, atomic helium, the hydrogen molecular ion, and the hydrogen molecule. These systems are not only bonded by the attractive Coulomb interactions, but also dissociated within an external field, e.g., an extensive laser field, In my thesis, both the bond and dissociation procedures are discussed in details. The homo-charged system contains some identical particles. These systems can be bonded only in some external fields by the repulsive Coulomb interaction, such as some ions in Paul trap. In this thesis, I studied the classical, semi-classical, and quantum dynamical behaviors of two, and three Paul trapped ions.The first part of my thesis describes the dissociation and ionization of the hydrogen molecular ion (H₂⁺) in an intense laser field. I first studied the classical and quantum dynamical behaviors of the hydrogen molecular ion in the field-free case. The quantum Schrodinger equations for the one- and two-dimensional h₂⁺ under the Born-Oppenheimer Approximation (BOA), the exact eigen energies, and the eigen wavefunctions in the serial forms were obtained. Then the number of the nodal lines within the wave functions was introduced to classify the eigen states. Classically, a...