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This book presents an analytical theory on the electronic states in low-dimensional systems and finite crystals recently developed by the author based on a differential equation theory approach. This theory gives some exact and general fundamental understandings on the electronic states in ideal low-dimensional systems and finite crystals such as the numbers and the behaviors of electronic states of different types; It provides new insights on some fundamental problems in low-dimensional systems such as surface states, quantum confinement effects etc, some of them are quite different from what are traditionally believed in the solid state physics community.
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.
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.
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 Schrodinger operator with truncated periodic potential. ... The book might be interesting to both physicists and mathematicians." (Aleksander Pankov, Zentralblatt MATH, Vol. 1105 (7), 2007)
