Methods and Applications of Analysis
Volume 17 (2010)
Semi-classical Analysis of a Conjoint Crossing of Three Symmetric Modes
Pages: 137 – 164
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.