On double eigenvalues of Schrödinger operators on two-dimensional tori (Q2368157)

Let \(\Gamma\) be a generic lattice in \(\mathbb{R}^ 2\) and let \(V\) be a potential in \(C^ \infty (\mathbb{R}^ 2/ \Gamma)\), \(N\in\mathbb{N}\) and \(\varepsilon>0\); then there exists a potential \(W\) in \(C^ \infty (\mathbb{R}^ 2/ \Gamma)\) such that \(| W|_ \infty \leq\varepsilon\) and \(-\Delta+V+W\) has at least \(N\) double eigenvalues.