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- W4300200423 abstract "We study the time-dependent Schrödinger equation with matrix-valued potential presenting a generic crossing of type B, I, J or K in Hagedorn's classification. We use two-scale Wigner measures for describing the Landau–Zener energy transfer which occurs at the crossing. In particular, in the case of multiplicity 2 eigenvalues, we calculate precisely the change of polarization at the crossing. Our method provides a unified framework in which codimension 2, 3 or 5 crossings can be discussed. We recover Hagedorn's result for wave packets, from Wigner measure point of view, and extend them to any data uniformly bounded in L 2 . The proof is based on a normal form theorem which reduces the problem to an operator-valued Landau–Zener formula." @default.
- W4300200423 created "2022-10-03" @default.
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- W4300200423 date "2003-12-01" @default.
- W4300200423 modified "2023-09-26" @default.
- W4300200423 title "WIGNER MEASURES AND MOLECULAR PROPAGATION THROUGH GENERIC ENERGY LEVEL CROSSINGS" @default.
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- W4300200423 doi "https://doi.org/10.1142/s0129055x03001904" @default.
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