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Search: MSC category 81Q10 ( Selfadjoint operator theory in quantum theory, including spectral analysis )

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1. CMB Online first

Dimassi, Mouez
Semi-classical asymptotics for Schrödinger operator with oscillating decaying potential
We study the distribution of the discrete spectrum of the Schrödinger operator perturbed by a fast oscillating decaying potential depending on a small parameter $h$.

Keywords:periodic Schrödinger operator, semi-classical asymptotics, effective Hamiltonian, asymptotic expansion, spectral shift function
Categories:81Q10, 35P20, 47A55, 47N50, 81Q15

2. CMB 2010 (vol 53 pp. 737)

Vougalter, Vitali
On the Negative Index Theorem for the Linearized Non-Linear Schrödinger Problem
A new and elementary proof is given of the recent result of Cuccagna, Pelinovsky, and Vougalter based on the variational principle for the quadratic form of a self-adjoint operator. It is the negative index theorem for a linearized NLS operator in three dimensions.

Categories:35Q55, 81Q10

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