Stuttgart 2012 – scientific programme
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A: Fachverband Atomphysik
A 19: Atomic systems in external fields II
A 19.1: Talk
Tuesday, March 13, 2012, 14:00–14:15, V57.05
Spectra of harmonium in a magnetic field using the Herman-Kluk propagator — •Frank Grossmann1 and Tobias Kramer2 — 1Institut für Theoretische Physik, Technische Universität Dresden, 01062 Dresden — 2Institut für Thoeretische Physik, Universität Regensburg, 93053 Regensburg
For two interacting electrons in a harmonic quantum dot and a constant magnetic field, we show that time-dependent semiclassical calculations using the Herman-Kluk initial value representation of the propagator [1] lead to eigenvalues of the same accuracy as WKB calculations with Langer correction [2]. The latter are restricted to integrable systems, however, whereas the time-dependent initial value approach allows for applications to high-dimensional, possibly chaotic dynamics and can be extended to arbitrary shapes of the potential. The Langer correction is not needed due to the fact that we are using Cartesian coordinates [3].
[1] M. Herman and E. Kluk, Chem. Phys. 91, 27 (1984)
[2] F. Grossmann and T. Kramer, J. Phys. A 44, 445309 (2011)
[3] G. van de Sand and J.-M. Rost, Phys. Rev. A 59, R1723 (1999)
This work was supported by the DFG through grants GR 1210/4-2 as well as KR 2889/2.