Electronic States in Crystals of Finite Size

Quantum Confinement of Bloch Waves

  • Shang Yuan Ren

Part of the Springer Tracts in Modern Physics book series (STMP, volume 270)

Table of contents

  1. Front Matter
    Pages i-xvi
  2. Why a Theory of Electronic States in Crystals of Finite Size Is Needed

    1. Front Matter
      Pages 1-1
    2. Shang Yuan Ren
      Pages 3-18
  3. One-Dimensional Semi-infinite Crystals and Finite Crystals

  4. Low-Dimensional Systems and Finite Crystals

    1. Front Matter
      Pages 89-89
    2. Shang Yuan Ren
      Pages 91-118
    3. Shang Yuan Ren
      Pages 119-144
  5. Epilogue

    1. Front Matter
      Pages 175-175
    2. Shang Yuan Ren
      Pages 177-187
  6. Back Matter
    Pages 189-283

About this book


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 confirmed in subsequent investigations by other authors on various relevant problems. In this new edition, the theory is further extended to one-dimensional photonic crystals and phononic crystals, and a general theoretical formalism for investigating the existence and properties of surface states/modes in semi-infinite one-dimensional crystals is developed. In addition, there are various revisions and improvements, including using the Kronig-Penney model to illustrate the analytical theory and make it easier to understand. This book is a valuable resource for solid-state physicists and material scientists.


Effective Mass Approximation Kronig-Penney Model One-dimensional phononic crystals One-dimensional photonic crystals Quantum confinement of Bloch waves Truncation of periodicity

Authors and affiliations

  • Shang Yuan Ren
    • 1
  1. 1.School of PhysicsPeking UniversityBeijingChina

Bibliographic information

  • DOI
  • Copyright Information Springer Nature Singapore Pte Ltd. 2017
  • Publisher Name Springer, Singapore
  • eBook Packages Physics and Astronomy
  • Print ISBN 978-981-10-4716-9
  • Online ISBN 978-981-10-4718-3
  • Series Print ISSN 0081-3869
  • Series Online ISSN 1615-0430
  • Buy this book on publisher's site
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