Abstract

In this thesis a fast, efficient and simple algorithm and its implementation (in the Java programming language) is presented; the algorithm calculates the energy states and the corresponding wave functions of a one-particle quantum well/wire/dot structure with an arbitrary potential profile by solving the multi-dimensional time-independent Schrödinger equation. The algorithm is based on the Finite Cloud Method (FCM), which is a truly meshless method. The contributions of this thesis are the expansion of FCM to a 3D method and implementing a tool to solve the multi-dimensional Schrödinger equation in an efficient way. To validate the accuracy and efficiency of our implementation we calculated the eigenstates of different rectangular GaAs quantum-wells, -wires and -dots. Comparing the obtained results with the analytical results published in the literature shows our approach to be a successful proof of concept. The results also confirm our implementation of the FCM algorithm to be highly accurate and efficient.