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9 Semiclassical Theory: Path Integrals
Fig. 9.4 Poincaré surface of
section of the phase space of
diamagnetic hydrogen for
m = 0 in the coordinate
frame (p r , p s , r, s), where
z = −2rs and ρ = r 2 − s 2 .
Plots are of p s versus s for
r = 0. (a) = −1.0. (b)
= −0.4. (c) = −0.3. (d)
= −0.1. Reproduced from
(Mao and Delos 1992) with
permission of the authors
Fig. 9.5 A plot of a chaotic trajectory in configuration space near the ionization threshold,
Reproduced from (Du and Delos 1988a) with permission of the authors
Ruder (1987); Friedrich and Wintgen (1989), and Hasagawa et al. (1989).) Eckhardt
and Wintgen (1990) have been able to classify the periodic orbits in diamagnetic
hydrogen. See also Beims and Alber (1993).
9.8.2 Absorption Cross Section
In the presence of a weak laser pulse, diamagnetic hydrogen will absorb photons and
can be excited from the ground state into some high-level excited states. A measure
of the efficiency of the process as a function of incident laser frequency is given by
the absorption cross section, which we now derive (Sakurai 1994). Let us assume