A generalized energy eigenvalue problem for effectively solving the confined electron states in quantum semiconductor structures via boundary integral analysis

This paper introduces a novel approach for the efficient determination of confined electron states in quantum semiconductor structures through the introduction of a generalized energy eigenvalue problem formulated within the framework of boundary integral analysis. The proposed method enables the direct determination of the energy eigenvalues and normalized wavefunctions for bound quantum states. The novel technique aims to address the challenges associated with efficiently modeling the behavior of electrons within confined regions, offering insights into optimizing the performance of a wide range of quantum semiconductor structures. By employing boundary integral techniques, the paper establishes a comprehensive numerical framework that accommodates the complexity of quantum confinement effects. The methodology is demonstrated through numerical simulations, showcasing its effectiveness and accuracy in predicting electron states within different quantum wire structures.