Methods and Applications of Analysis

Volume 17 (2010)

Number 2

Semi-classical Analysis of a Conjoint Crossing of Three Symmetric Modes

Pages: 137 – 164



Clotilde Fermanian Kammerer

Vidian Rousse


In this article we focus on a semiclassical Schrödinger equation with matrix-valued potential presenting a symmetric conjoint crossing of three eigenvalues. The potential we consider is well-known in the chemical literature as a pseudo Jahn-Teller potential. We analyze the energy transfers which occur between the three modes in terms of Wigner measures.


Semi-classical analysis; Born-Oppenheimer approximation; Schrödinger equation; Wigner measures; eigenvalue crossings

2010 Mathematics Subject Classification

Primary 35Q40. Secondary 35B27, 81Q20.

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