The construction of basis functions for modelling closed- and open quantum wire problems

Modelling the electronic behaviour of periodic quantum wire structures has attracted considerable attention and significant results have been achieved. Nearly exclusively, the utilised methods are based on the concept of the effective mass approximation. The main objective in this paper is to propose a novel methodology which directly solves the Schro¿dinger equation, allowing to obtain exact solutions for arbitrary, periodic quantum wire structures. The Brillouin band diagram has been computed for an important model problem and tested with the numerical results associated with limiting structures. The calculated underlying eigenstate solutions are interesting for their own sake. However, and more importantly, the computed eigenfunctions have been determined to serve as 2D limiting cases for future 3D structures, which are the subject of our ongoing research.