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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.
List of contents
Why a Theory of Electronic States in Crystals of Finite Size is Needed.- One-Dimensional Semi-infinite Crystals and Finite Crystals.- Mathematical Basis.- Surface States in One-Dimensional Semi-infinite Crystals.- Electronic States in Ideal One-Dimensional Crystals of Finite Length.- Low-Dimensional Systems and Finite Crystals.- Electronic States in Ideal Quantum Films.- Electronic States in Ideal Quantum Wires.- Electronic States in Ideal Finite Crystals or Quantum Dots.- Epilogue.- Concluding Remarks.
About the author
The author has been working in various areas in the field of theoretical condensed matter physics for more than twenty years and has published more than ninety research papers. Some of them are well cited.
Summary
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.
Additional text
From the reviews:
"The book is devoted to the theory of electronic states in crystal that have finite size. Mathematically, this reduces to spectral theory of Schrödinger operator with truncated periodic potential. … The book might be interesting to both physicists and mathematicians." (Aleksander Pankov, Zentralblatt MATH, Vol. 1105 (7), 2007)
Report
From the reviews:
"The book is devoted to the theory of electronic states in crystal that have finite size. Mathematically, this reduces to spectral theory of Schrödinger operator with truncated periodic potential. ... The book might be interesting to both physicists and mathematicians." (Aleksander Pankov, Zentralblatt MATH, Vol. 1105 (7), 2007)
