Abstract
The reduction scheme, which is the standard tool of the analytic theory of perturbations [Ka], has been recently extended to the time time dependent case; for the case when the small parameter lies in the front of the time derivative (the adiabatic case) [Ne4] and also for the case H(t) = H 0+ɛV(t) [MN1].
In what follows, we shall first review, following [Ne4], [Ne5] the main facts about adiabatic reduction theory, and then apply it to obtain [MN2] the semi-classical (Born-Oppenheimer) behaviour of the S matrix for the restate one-dimensional Schrödinger operator. On the way a rigorous derivation of the so-called “trajectory model” is given.
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© 1994 Springer Basel AG
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Nenciu, G. (1994). Adiabatic Reduction Theory. Semiclassical S-matrix for N-state one-dimensional systems. In: Demuth, M., Exner, P., Neidhardt, H., Zagrebnov, V. (eds) Mathematical Results in Quantum Mechanics. Operator Theory: Advances and Applications, vol 70. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8545-4_37
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DOI: https://doi.org/10.1007/978-3-0348-8545-4_37
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