Electron Energy Spectra

This textbook represents results gathered in the last half decade of study. It presents many essential aspects from the domain of advance elements of the theory of solid state physics, especially focused on discrete spaces and their connection with the influence of external electric
and magnetic fields. Beside its orientation to the analytical aspects it also touches the computational aspect of the interpretations.
Topics such as: periodic potentials, energy bands and gaps, energy dispersion and approximation models are examined analytically as well as numerically. The various subjects debated are meticulously arranged into a balanced content and into a progressive approach from simple to complex. The electron energy spectra are presented from a new perspective, from which to evolve a practical method of investigation.
From a didactical point of view the content of this book, as a monograph item, is placed at the frontier between a treatise and a textbook; mainly because it combines the expounds of the conceptual basics along with its correspondent theoretical experiments and explains in a gradual manner high level of knowledge.
Regarding the evaluation of the numerical results it has been made an effort to select representatives from a tremendously by great quantity of computations. It is clear that this book is not for those unfamiliar with the elementary descriptive facts related to the solid state theory,
such as the Kronig-Penney model, the tight-binding approximation and the Harper model. All of these represent the foundation of the later description regarding the electron energy spectra. Without any of these lectures it may become difficult or even impossible to understand.
Thus, the complete each introduction into the themes, along with its contents related to the numerical results which sustain any analytical investigation, can therefore be of a significant value for: 1. Graduate students interested in deepening their knowledge of the solid state terrain, connected to the study of discrete systems and of course of the influence of external fields. This book should improve their visions and may offer a leading path for their own research in these domains.
2. Engineers and scientists wiling to update their noesis, regarding solid state physics on discrete spaces. The latest discoveries in the domain of interest are presented through each chapter, in an informative and comprehensive way.
3. Last but not least, the book addresses IT mathematicians specialized in numerical computation along with simulations interests. Mainly, due to the fact that the numerical computations represent a powerful tool and a costless method of investigation, especially in the mesoscopic research area.
The selection of topics obviously bears the stamp of our research interest. Some themes related to the thermal, statistical aspects, the transport problems or even the optical perspectives have been omitted. In order to clarify some of the boundary problems, there are listed in Appendix along with the Fourier transformation. Finally, I want to mention that I am indebted to the Scientific WorkPlace 5.5 integration platform of LaTeX Typesetting, to Mathematica 8.0 - as the ultimate application for computations, to MapleTM 14.0 - for the essential technical computing software and Matlab - the language of technical computing, for their help in my computational research.
Timisoara
November 2010
Ovidiu Borchin