Wavelet‐Based Adaptive Computations of the Excitonic Eigenstates of Disordered Semiconductor Quantum Wires

A novel adaptive wavelet based method is presented that allows us to compute eigenvalues and eigenvectors of the electronic Schrödinger equation. Our method outperforms direct discretization methods with equidistant grid spacings, in particular, for problems that involve several length scales. As an application we present numerical evaluations of the energetically lowest exciton states for ordered and disordered semiconductor quantum wires.