Recent experiments [E. M. Spain et al., J. Chem. Phys 102. 24 (1995)] discovered alignment effects in cross sections for near-resonant energy-transfer collisions of Xe atoms with Ca Rydberg atoms at a single mean relative velocity. A collaborative quantum-mechanical stud; [W. Issacs and M. A. Morrison. Phys. Rev. A, 57, R9 (1993)] confirmed these findings and discovered pronounced oscillations in the velocity dependence of state-to-state cross sections. Collisions corresponding to the 17d(m0)--> 18p(m) transitions in the Ca-He system are here analyzed semiclassically. This analysis shows that the origin of these oscillations is a phase interference process unique to Rydberg target states. We further demonstrate the importance of retaining the energy defect and of using quantum-defect phase-shifted radial functions in calculations of alignment cross sections for Rydberg states.

The Fourier-grid (FG) method is a recent L2 variational treatment of the quantum mechanical eigenvalue problem that does not require the use of a set of basis functions: it is rather a discrete variable representation approach. The author restates the FG philosophy in more general terms, examine and compare this method with other approaches to the eigenvalue problem, and begin the development of an FG R-matrix method for scattering. The philosophy of the FG method is to use the simplest representation for each of the kinetic and potential energy operators of the Hamiltonian, and use a generalized Fourier transform to put the matrix elements of one of the above operators in the same representation as the other, so the Hamiltonian has a single representation. Thus, the Hamiltonian is represented at discrete points in either configuration or its reciprocal space.

The authors present the latest developments in the Fourier-grid R-matrix theory of scattering. These developments are based on the generalized Fourier-grid formalism and use a new type of extended discrete Fourier transform: the discrete Fourier-Riccati-Bessel transform. They apply this new R-matrix approach to problems of potential scattering, to demonstrate how this method reduces computational effort by incorporating centrifugal effects into the representation. As this technique is quite new, they have hopes to broaden the formalism to many types of problems.

A variational procedure without the need of using L2 basis set expansion or trial wave functions is introduced for efficient and accurate treatment of relativistic quantum-mechanical eigenvalue problems. The method, based on the extension of the Fourier-grid Hamiltonian technique, is free from the problems of variational collapse, Further, the procedure does not require the computation of potential matrix elements and the eigenvectors provide directly the amplitude of wave functions at the space grid points. The simplicity and accuracy of the method is illustrated for a case study of the Dirac-Coulomb-field equation.

In this paper we accomplish three goals. First, we present new nonperturbative results of complex quasi-energies (shifts and widths) for several low-lying excited states of atomic H in strong fields, using the L2 non-Hermitian Floquet matrix technique. Second, we present a new nonperturbative L2 technique for the treatment of ac Stark shifts of arbitrary excited states. We found that all the Rydberg states in weak fields are upshifted and closely follow the quadratic field dependence described by the ponderomotive potential e2F2/4mω2. Large deviation from the ponderomotive shift and intricate level-shift behaviors, however, occur in strong fields. Finally, we present a classical nonperturbative treatment of the electronic motion in intense laser fields. We show that the spectral analysis of classical trajectories can provide detailed insights regarding the mechanisms responsible for the multiple-harmonic generation recently observed in high-intensity experiments.

We present a generalized version of the Feynman-Vernon-Hellwarth geometric representation and a biorthogonal density matrix formalism for the description of the non-Hermitian Schrödinger equation. The theory is applied to the study of complex geometric quantum phases in dissipative systems. It is shown that the complex Aharonov-Anandan (AA) geometric phase is related to the complex solid angle enclosed by a complex Bloch vector trajectory S(t). General analytic formulas are presented for the complex AA phase for a driven dissipative two-level system undergoing multiphoton Rabi floppings.