Iterative projection methods for computing relevant energy states of a quantum dot

A computational technique for computing relevant energy levels and corresponding wave functions of an electron confined by a 3D quantum dot embedded in a semiconductor matrix are studied. Assuming an energy and position dependent electron effective mass approximation this problem is governed by a rational eigenvalue problem. We discuss the application of iterative projection method of Arnoldi and Jacobi–Davidson type. Projected problems of small dimension are solved efficiently by safeguarded iteration.