CNS
Meeting
Monday Nov 10, 11:00 AM, W505 Howey
Semiclassical quantization with bifurcating orbits
Thomas Bartsch
Closed-orbit theory provides a semiclassical description of atomic
photo-absorption spectra that is similar to semiclassical trace formulas. It is
plagued by the same fundamental difficulties: The spectrum is represented as a
divergent infinite sum over classical orbits, and the contribution of an
individual orbit diverges when the orbit undergoes a bifurcation. While the
latter problem can be overcome by uniform approximations, their use prevents
the computation of individual semiclassical spectral lines. Taking as examples
the hydrogen atom in an electric field and in crossed electric and magnetic
fields, I will demonstrate that the technique of harmonic inversion allows the
inclusion of uniform approximations into a high-resolution semiclassical
quantization, and I will describe the construction of uniform approximations
and some pertinent open problems.