Coupling of the continuum and semiclassical limit. Part I: convergence of eigenvalues

Matthias Keller, Lorenzo Pettinari, Christiaan J. F. van de Ven

We analyze the semiclassical $d$-dimensional Schrödinger operator in the continuum $\frac{1}{2}\Delta +{\lambda }_N^{2}V$ discretized on a mesh with spacing proportional to $1/N$. The semi-clas…