# Eigenvalue splitting for a system of Schr\"odinger operators with an energy-level crossing.

@article{Assal2019EigenvalueSF, title={Eigenvalue splitting for a system of Schr\"odinger operators with an energy-level crossing.}, author={Marouane Assal and Setsuro Fujii'e}, journal={arXiv: Mathematical Physics}, year={2019} }

We study the asymptotic distribution of the eigenvalues of a one-dimensional two-by-two semiclassical system of coupled Schrodinger 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 $h\to 0^+$. In particular, in the symmetric case, the eigenvalue splitting occurs and we prove that…

## 2 Citations

### Resonance free domain for a system of Schrödinger operators with energy-level crossings

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We consider a $2\times 2$ system of 1D semiclassical differential operators with two Schrodinger operators in the diagonal part and small interactions of order $h^\nu$ in the off-diagonal part, where…

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We analyze the eigenvalue problem for the semiclassical Dirac (or Zakharov–Shabat) operator on the real line with general analytic potential. We provide Bohr–Sommerfeld quantization conditions near…

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