Semiclassical Approximations in Phase Space with Coherent States

We present a complete derivation of the semiclassical limit of the coherent state propagator in one dimension, starting from path integrals in phase space. We show that the arbitrariness in the path integral representation, which follows from the overcompleteness of the coherent states, results in many different semiclassical limits. We explicitly derive two possible semiclassical formulae for the propagator, we suggest a third one, and we discuss their relationships. We also derive an initial value representation for the semiclassical propagator, based on an initial gaussian wavepacket. It turns out to be related to, but different from, Heller's thawed gaussian approximation. It is very different from the Herman--Kluk formula, which is not a correct semiclassical limit. We point out errors in two derivations of the latter. Finally we show how the semiclassical coherent state propagators lead to WKB-type quantization rules and to approximations for the Husimi distributions of stationary states.Comment: 80 pages, 4 figure

Excitation of weakly bound Rydberg electrons by half-cycle pulses

The interaction of a weakly bound Rydberg electron with an electromagnetic half-cycle pulse (HCP) is described with the help of a multidimensional semiclassical treatment. This approach relates the quantum evolution of the electron to its underlying classical dynamics. The method is nonperturbative and is valid for arbitrary spatial and temporal shapes of the applied HCP. On the basis of this approach angle- and energy-resolved spectra resulting from the ionization of Rydberg atoms by HCPs are analyzed. The different types of spectra obtainable in the sudden-impact approximation are characterized in terms of the appearing semiclassical scattering phenomena. Typical modifications of the spectra originating from finite pulse effects are discussed.Comment: Submitted to Phys. Rev.

How to Stimulate Single Mothers on Welfare to Find a Job: Evidence from a Natural Experiment

We present the results from a natural experiment in which single mothers on welfare were stimulated to find a job. Two policy instruments were introduced: an earnings disregard and job creation. The experiment was performed at the level of municipalities in The Netherlands, a country with relatively high benefits and low incentives for single mothers to leave welfare for work. In our analysis, we make a distinction between native and immigrant welfare recipients. For immigrant single mothers and some groups of native single mothers we find a positive employment effect of an earnings disregard. Job creation in addition to the earnings disregard increased working hours for some groups of single mothers. Although the outflow from welfare was not affected, welfare expenditures were reduced