A boundary integral framework for formulating a generalized eigenvalue problem to efficiently compute confined electron states in quantum dot structures

This study presents an innovative method for efficiently determining confined electron states in quantum dot structures by formulating a generalized energy eigenvalue problem within the boundary integral framework. The proposed approach directly computes energy eigenvalues and normalized wavefunctions for both infinitely and finitely bound quantum states. It aims to overcome challenges in accurately modeling electron behavior in confined regions, providing valuable insights for optimizing quantum semiconductor structures. By utilizing boundary integral techniques, this method establishes a robust numerical framework to address the complexities of quantum confinement effects. Numerical simulations demonstrate the effectiveness and accuracy of the proposed technique in determining electron states for quantum dot structures.