Abstract
We discuss the exact solution of the time-dependent Schrödinger equation for a system of two crossing levels with a residual interaction. In contrast to the familiar Landau-Zener (LZ) solution used in most applications, we allow for more general boundary conditions; in particular we treat explicitly the case of afinite interval around the crossing point. The exact jumping probability is shown to be extremely sensitive to these boundary conditions; in many realistic cases it is found to be smaller than the LZ value by several orders of magnitude. We also compare the exact excitation energy to the one obtained in the usual cranking approach.
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Work supported in parts by GSI Darmstadt
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Góźdź, A., Werner, E. & Brack, M. Non-adiabatic effects in the time dependent level crossing problem. Z Physik A 319, 159–165 (1984). https://doi.org/10.1007/BF01415629
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DOI: https://doi.org/10.1007/BF01415629