Geometric tools of the adiabatic complex WKB method

Alexander Fedotov (1) , Frédéric Klopp (2)

1 Department of Mathematical Physics - Department of Mathematical Physics
2 LAGA - Laboratoire Analyse, Géométrie et Applications

The paper is devoted to the description of the main geometric and analytic tools of a complex WKB method for adiabatic problem. We illustrate their use by numerous examples.

Mots clés: Periodic Schrödinger equation; adiabatic perturbations; asymptotics of solutions; complex WKB method

Domaines: Physique mathématique [math-ph]; Théorie spectrale [math.SP]; Equations aux dérivées partielles [math.AP]

Alexander Fedotov, Frédéric Klopp. Geometric tools of the adiabatic complex WKB method. 2003. ⟨hal-00000329⟩