The microlocal Landau-Zener formula
The projected single-particle Dirac operator for Coulombic potentials.
The quantum stability problem for time-periodic perturbations of the harmonic oscillator
The return of the quartic oscillator. The complex WKB method
The role of locality in perturbation theory
The time-dependent Born-Oppenheimer approximation
We explain why the conventional argument for deriving the time-dependent Born-Oppenheimer approximation is incomplete and review recent mathematical results, which clarify the situation and at the same time provide a systematic scheme for higher order corrections. We also present a new elementary derivation of the correct second-order time-dependent Born-Oppenheimer approximation and discuss as applications the dynamics near a conical intersection of potential surfaces and reactive scattering.