High-order eigenstate calculation of arbitrary quantum structures

Quantum engineering of electronic energy states using nanoscale layers of semiconductor compounds allows the design and the observation of quantum phenomena which are typically observed in atomic structures. Furthermore, semiconductors are present in nearly all modern electronic devices and are a crucial component of integrated circuits. Due to the relatively high rate of manufacturing defects, it is crucial to have a method for testing new semiconductor formations without requiring a sample to be fabricated. A simple, fast and very accurate numerical technique is presented to calculate the eigenstates of such arbitrary quantum structures. The method is based on a high-order finite difference scheme which allows the use of sparse matrix algebra, thus, significantly reducing computational time and allowing for high precision results even for the high energy states