2019/10/02 by Assal, Marouane, Fujiié, Setsuro
#FOS: Physical sciences #Mathematical Physics (math-ph)
paper · doi:10.48550/arxiv.1910.01195
We study the asymptotic distribution of the eigenvalues of a one-dimensional two-by-two semiclassical system of coupled Schrödinger operators in the presence of two potential wells and with an energy-level crossing. We provide Bohr-Sommerfeld quantization condition for the eigenvalues of the system on any energy-interval above the crossing and give precise asymptotics in the semiclassical limit h→ 0+. In particular, in the symmetric case, the eigenvalue splitting occurs and we prove that the splitting is of polynomial order h\frac32 and that the main term in the asymptotics is governed by the area of the intersection of the two classically allowed domains.