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Journal of physics. A, Proceedings of the Physical Society. General

Variational trial functions in quantum theory. II. Continuous spectrum

T. L. John, K L Williams

Published Aug 1, 1972• 0 citations
Publisher

Abstract

For Pt.I see ibid., vol.5, 1152 (1972). A method given in Part I for the calculation of variational trial functions is applied to the continuous spectra of some simple one and two particle systems.
DOI
10.1088/0305-4470/5/8/009

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For pt.I see ibid., vol.20, p.397-409, 1987. The spectrum of an ellipsoidal box of prolate and oblate symmetry are calculated by an extract diagonalisation and by semiclassical methods. The influence of a separatrix in phase space is analysed with the help of the WKB phases derived in an earlier paper. Differences between the prolate the oblate L z =0 states are explained using this separatrix. It is found that the EBK method, improved by the uniform approximation, leads to a spectrum in very good agreement with the wave mechanical results. The spectrum of a two-dimensional elliptical membrane ('billiard' box) is also studied with similar conclusions.
For pt.I see ibid., vol.28, p.5057-75 (1995). In the previous paper, a non-perturbative time-dependent theory of resonant multiphoton ionization by both smooth and rectangular pulses was derived, and as a first step, applied to the two-photon ionization of caesium in weak fields. In the present paper, we continue the analysis of the same system, extending the weak-field results and considering the case of stronger fields. At higher intensities the spectra exhibit energy modulations of a different character from those predicted for low power. Here, for stronger fields, the structure arises from Rabi oscillations, which, for the smooth pulses assumed here, are triggered by time-dependent Stark shifts. In order to obtain a better understanding of the energy oscillations, we also look at the photoelectron energy spectrum produced by a rectangular pulse, a problem which is solved exactly. We show that there are other sources of strong-field structure.