A Quantum Element Reduced Order Model

A reduced-order model for quantum eigenvalue problems developed previously is revised and combined with the domain decomposition method to construct the quantum element method (QEM). The basic idea of the QEM is to partition a quantum domain structure into several subdomains or elements. Each element is projected onto a functional space using the proper orthogonal decommission. These elements are then combined together to construct the whole domain structure. The proposed QEM has been demonstrated in 2 quantum well structures constructed with several elements. The study illustrates that the QEM is capable of offering accurate prediction of wave functions and quantum eigenenergies with a substantial reduction in the numerical degrees of freedom compared to direct numerical simulation of the Schrödinger equation.