Electronic States in Crystals of Finite Size: Quantum confinement of Bloch waves (Springer Tracts in Modern Physics)

The theory of electronic states in the traditionally solid state physics is essentially a theory of electronic states in crystals of infinite size. However, any real crystal always has a finite size. This book presents an analytical theory on the electronic states in ideal low-dimensional systems and finite crystals recently developed by the author based on a differential equation theory approach. It gives some exact and general fundamental understandings on the electronic states in ideal low-dimensional systems and finite crystals and provides new insights on some fundamental problems in low-dimensional systems such as the surface states, quantum confinement effects etc, some of them are quite different from what are traditionally believed in the solid state physics community. 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 properties of electronic states in real crystals of ?nite size has both theoretical and practical signi?cance. Many years ago when the author was a student learning solid state physics at Peking University, he was bothered by a feeling that the general use of the periodic boundary conditions seemed unconvincing. At least the e?ects of such a signi?cant simpli?cation should be clearly understood. Afterward, he learned that many of his school mates had the same feeling. Among many solid state physics books, the author found that only in the classic book Dynamic Theory of Crystal Lattices by Born and Huang was there a more detailed discussion on the e?ects of such a simpli?cation in an Appendix. The theory of electronic states in crystals in traditional solid state physics is essentially a theory of electronic states in crystals of infinite size. However, any real crystal always has a finite size. This book presents an analytical theory on the electronic states in ideal low-dimensional systems and finite crystals, recently developed by the author, based on a differential equation theory approach. It gives some exact and general fundamental understandings on the electronic states in ideal low-dimensional systems and finite crystals, and provides new insights into some fundamental problems in low-dimensional systems such as the surface states, quantum confinement effects, etc., some of which are quite different from what is traditionally believed in the solid state physics community. Front Matter....Pages I-XIV Front Matter....Pages 1-1 Introduction....Pages 3-20 Front Matter....Pages 21-21 Mathematical Basis....Pages 23-47 Surface States in One-Dimensional Semi-infinite Crystals....Pages 49-63 Electronic States in Ideal One-Dimensional Crystals of Finite Length....Pages 65-85 Front Matter....Pages 87-87 Electronic States in Ideal Quantum Films....Pages 89-115 Electronic States in Ideal Quantum Wires....Pages 117-142 Electronic States in Ideal Finite Crystals or Quantum Dots....Pages 143-170 Front Matter....Pages 171-171 Concluding Remarks....Pages 173-182 Back Matter....Pages 183-204 "This book presents an analytical theory on the electronic states in ideal low-dimensional systems and finite crystals, recently developed by the author, based on a differential equation theory approach. It gives some exact and general fundamental understandings on the electronic states in ideal low-dimensional systems and finite crystals, and provides new insights into some fundamental problems in low-dimensional systems such as the surface states, quantum confinement effects, etc., some of which are quite different from what is traditionally believed in the solid state physics community."--Jacket