A mathematical treatment is presented of the known Berry, Wilczek-Zee, Aharonov-Anandan, and Pancharatnam topological phases, and simple illustrative examples of their quantum mechanics are presented. The continuity and connection is traced among the various phases, while filling the gap involved with the forgotten works of S. M. Rytov and V. V. Vladimirskii in polarization optics. A set of current experiments in polarization optics where the topological phases are measured is discussed in detail. Additional information on recently obtained results involving manifestations of geometrical phases in quantum mechanics and other fields of physics is contained in the Appendix and in the studies cited there.

We consider the time delay of electron detachment from a Coulomb center and two-center systems in the process of ionization. It is shown that the attosecond streaking, most usual method of time delay measure, can be formally described by placing a virtual detector of the arrival time delay at a certain distance from the center of the system. This approach allows derivation of a simple formula for Coulomb-laser coupling that perfectly agrees with the results of numerical solution of the time-dependent Schrödinger equation. The dependence of the time delay upon the energy, the angular momentum projection, and the azimuthal quantum number is studied for the ionization of molecular hydrogen ion. Finally, we propose a physical interpretation of singularities, arising when the formal expression for the time delay is applied to the ionization of molecular hydrogen.

No abstract

The multifold differential cross section of the ionization of hydrogen molecular ion by fast-electron impact is calculated by a direct approach, which involves the reduction of the initial six-dimensional ͑6D͒ Schrödinger equation to a 3D evolution problem followed by the numerical modeling of the wave-packet dynamics. This approach avoids the use of stationary Coulomb two-center functions of the continuous spectrum of the ejected electron that demands cumbersome calculations. The results obtained, after verification of the procedure in the case of atomic hydrogen, reveal interesting mechanisms in the case of small scattering angles.

No abstract