Two-electron states: Phys. Rev. A 4, 207 (1971) which
derived wave functions and the quantum-mechanical threshold law for
two slow electrons escaping from a positive ion. This paper revived
interest in the Wannier threshold law derived by Wannier classically
in 1953 but essentially forgotten after that, and gave rise to
tremendous activity, both experimentally and theoretically, in the
last 30 years.
Comm. At. Mol. Phys. 14, 285 (1984) gave a unified presentation
of two-body and three-body threshold laws in atomic, nuclear and
condensed matter physics.
J. Phys. B 16, L699 (1983) described a new kind of "pair-Rydberg"
autoionizing states with a Bohr-Rydberg like spectrum which are
associated with the Wannier threshold law. This too has attracted
much subsequent experimental and theoretical work by groups across
the world. Wannier theory is now seen as central to the understanding
of electron correlations and to intermediate-energy electron-atom
scattering.
Science 258, 1444 (1992) is a unified view of the excitation and
decay of highly correlated states, whether of many electrons,
nucleons, or quarks.
Rydberg states in external fields: Phys. Rev. A 16, 613
(1977) and J. Phys. B 12, L193 (1979) pointed out the general
phenomena of "strong mixing" when two fields are equally important in
controlling an electron's motion. Characteristic resonances appear
near zero energy.
Phys. Rev. Lett. 63, 244 (1989), Phys. Rev. A 42, 6342 (1990),
and Rev. Mod. Phys. 64, 623 (1992) gave a common treatment of
degenerate perturbations that underlie the phenomena described above,
all such problems mapping onto the asymmetric rotor.
Phys. Rev. Lett. 26, 1136 (1971), Phys. Rev. A 11, 1865 (1975),
and Astrophys. J. 207, 671 (1976) treated a related problem, the
structure of atoms and matter in the intense magnetic fields that
exist on pulsars.
Quantum Defect Theory for Collisions and Spectroscopy:
Phys. Rev. A 26, 2441 (1982), Phys. Rev. A 38, 2255 (1988), and the
book Atomic Collisions and Spectra (U. Fano and A. R. P. Rau, 1986)
present a unified view of bound states, resonances and scattering in
multi-channel problems, applicable to any combination of short-range
and general long-range fields. Together with the work of the Seaton
school, this "Multi-channel Quantum Defect Theory" is now widely used
in atomic and molecular physics for analyzing complex spectra.
Group Theory and Symmetries: Rep. Prog. Phys. 53, 181
(1990) gave a common group-theoretical description of the phenomena
that are the subject of #1-6 above.
The book, Symmetries in Quantum Physics (U.Fano and
A.R.P.Rau, 1996), presents symmetries of rotations and
reflections and the Racah-Wigner algebra for quantum-mechanical
angular momentum, higher invariance and non-invariance group
symmetries in atomic, nuclear and particle physics, and applications
to multi-particle dynamics.
Variational Principles: J. Math. Phys. 13, 1797 (1972),
Phys. Rev. A 8, 662 (1973), and Rev. Mod. Phys. 55, 725 (1983) give a
very general procedure for constructing variational principles and
identities for almost any problem in mathematical physics. All the
known variational principles are easily recovered and new ones can be
derived by this simple constructive procedure. There have been wide
applications of this method.
Unitary Integration of time-dependent operator equations:
Phys. Lett. A 222, 304 (1996) and Phys. Rev. Lett. 81, 4785 (1998)
advance a very simple, general method for integrating a wide class of
time-dependent operator equations. The problem is reduced to solving
a single classical Riccati equation and the rest is simple algebra.
Already, problems of interest in laser-atom interactions, in quantum
optics, and in magnetic resonance phenomena (coupled qubits) have
been treated in this formalism (Phys. Rev. A 61, 032301 (1-5), 2000).
Recently, the method has also been extended to include dissipation
and decoherence (Phys. Rev. Lett. 89, 220405 (1-4), 2002) and several three- and four-level problems Phys. Rev. AA, 062316 and 063822 (2005). A compact, iterative scheme has been developed for reducing an U(N) problem of a N-level system in a manner similar to the Block sphere description from SU(2), and geometric phasas have been extracted: Phys. Rev. A74, 030304(R) (2006).
