Perturbatively unstable eigenvalues of a periodic Schrödinger operator
Let \(\Gamma\) be a lattice of maximal rank in \(\mathbb{R}^ d\), \(d\leq3\). For \(q\in L^ 2(\mathbb{R}^ d/\Gamma)\) the spectrum of \(-\Delta+2ik\nabla-k^ 2+q\) acting on \(L^ 2(\mathbb{R}^ d/\Gamma)\) is called the Floquet spectrum of \(q\) with crystal momentum \(k\). The authors investigate stability of Floquet eigenvalues of \(q\) and approximation of eigenfunctions by quasimodes.
approximation of eigenfunctions by quasimodes
scientific article; zbMATH DE number 57096