“…then one has to expect that the coupling εF 12 (x * )η is either singular or approximately of the order one with respect to ε, and one obtains leading order non-adiabatic transitions between the eigenspaces. These transitions, which are ubiquituous for polyatomic molecules and explain spectacular chemical reactions as for example the first step of vision (the cis-trans isomerization of retinal in rhodopsin), have been discussed for the propagation of Hagedorn wave packets through actual crossings by Hagedorn (1994) and through avoided crossings in (Hagedorn 1998a, Hagedorn and Joye 1999a, Bourquin, Gradinaru and Hagedorn 2012. With respect to general initial data, the propagation of expectation values through conical intersections has been carried out in (Fermanian-Kammerer and Gérard 2002, Lasser and Teufel 2005, Fermanian Kammerer and Lasser 2008, while avoided crossings have been considered in (Fermanian Kammerer and Lasser 2017).…”