The theory of electronic states in crystals is the very basis of modern solid state physics. In traditional solid state physics - based on the Bloch theorem - the theory of electronic states in crystals is essentially a theory of electronic states in crystals of in?nite size. However, that any real crystal always has a ?nite size is a physical reality one has to face. The di?erence between the electronic structure of a real crystal of ?nite size and the electronic structure obtained based on the Bloch theorem becomes more signi?cant as the crystal size decreases. A clear understanding of the...

This book presents an analytical theory of the electronic states in ideal low dimensional systems and finite crystals based on a differential equation theory approach. It provides precise and fundamental understandings on the electronic states in ideal low-dimensional systems and finite crystals, and offers new insights into some of the basic problems in low-dimensional systems, such as the surface states and quantum confinement effects, etc., some of which are quite different from what is traditionally believed in the solid state physics community. Many previous predictions have been...