Hydrogen atom in a magnetic field: Ghost orbits, catastrophes, and uniform semiclassical approximations
- Institut fuer Theoretische Physik I, Ruhr-Universitaet Bochum, D-44780 Bochum (Germany)
Applying closed-orbit theory to the recurrence spectra of the hydrogen atom in a magnetic field, one can interpret most, but not all, structures semiclassically in terms of closed classical orbits. In particular, conventional closed-orbit theory fails near bifurcations of orbits where semiclassical amplitudes exhibit unphysical divergences. Here we analyze the role of ghost orbits living in complex phase space. The ghosts can explain resonance structures in the spectra of the hydrogen atom in a magnetic field at positions where no real orbits exist. For three different types of catastrophes, viz. fold, cusp, and butterfly catastrophes, we construct uniform semiclassical approximations and demonstrate that these solutions are completely determined by classical parameters of the real orbits and complex ghosts. {copyright} {ital 1997} {ital The American Physical Society}
- OSTI ID:
- 467341
- Journal Information:
- Physical Review A, Vol. 55, Issue 3; Other Information: PBD: Mar 1997
- Country of Publication:
- United States
- Language:
- English
Similar Records
Recurrence spectroscopy: Observation and interpretation of large-scale structure in the absorption spectra of atoms in magnetic fields
Prebifurcation periodic ghost orbits in semiclassical quantization