The increasing interest in non-linear eigenvalue problems has once again caught the attention of the international scientific community, due to new and inexhaustible applications. The Quadratic Eigenvalue Problem currently receives more attention due to its great diversity and wide possibilities of application, such as the dynamic analysis of structural mechanisms, the study and description of acoustic systems, electrical circuit simulation, fluid mechanics, signals processing, and more recently, the nanoelectronic modeling of mechanical systems and the study of quantum transport of holes. The problem of quantum transport of charge carriers (electrons and holes) is narrowly Iinked to the study of spectral properties in heavy and light hole tunneling in semiconductor quantum heterostructures, as the appreciation of the fundamental transport properties of these materials can be directly applied to the analysis, design and functioning of practically all device structures that are currently technologically important.