## Landau-Zener transitions through small electric eigenvalue gaps in the Born-Oppenheimer approximation.(English)Zbl 0915.35090

The authors study the quantum evolution associated to a molecular Schrödinger operator, in the Born-Oppenheimer limit where the mass of the nuclei tends to infinity. Assuming that the electronic levels present a gap which tends to $$0$$ as the mass of the nuclei tends to infinity, they show that the corresponding transition probabilities are given by the Landau-Zener formula.

### MSC:

 35Q40 PDEs in connection with quantum mechanics 81V55 Molecular physics

### Keywords:

avoided crossings; transition probability; wave packets
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