Wave Equations in Higher Dimensions

  • Shi-Hai Dong

Table of contents

  1. Front Matter
    Pages I-XXV
  2. Introduction

    1. Front Matter
      Pages 1-1
    2. Shi-Hai Dong
      Pages 3-9
  3. Theory

    1. Front Matter
      Pages 11-11
    2. Shi-Hai Dong
      Pages 13-38
    3. Shi-Hai Dong
      Pages 51-59
  4. Applications in Non-relativistic Quantum Mechanics

    1. Front Matter
      Pages 65-65
    2. Shi-Hai Dong
      Pages 67-79
    3. Shi-Hai Dong
      Pages 81-96
    4. Shi-Hai Dong
      Pages 97-108
    5. Shi-Hai Dong
      Pages 119-128
  5. Applications in Relativistic Quantum Mechanics

    1. Front Matter
      Pages 155-155
    2. Shi-Hai Dong
      Pages 157-179
    3. Shi-Hai Dong
      Pages 203-218

About this book

Introduction

Higher dimensional theories have attracted much attention because they make it possible to reduce much of physics in a concise, elegant fashion that unifies the two great theories of the 20th century: Quantum Theory and Relativity. This book provides an elementary description of quantum wave equations in higher dimensions at an advanced level so as to put all current mathematical and physical concepts and techniques at the reader’s disposal. A comprehensive description of quantum wave equations in higher dimensions and their broad range of applications in quantum mechanics is provided, which complements the traditional coverage found in the existing quantum mechanics textbooks and gives scientists a fresh outlook on quantum systems in all branches of physics.
In Parts I and II the basic properties of the SO(n) group are reviewed and basic theories and techniques related to wave equations in higher dimensions are introduced. Parts III and IV cover important quantum systems in the framework of non-relativistic and relativistic quantum mechanics in terms of the theories presented in Part II. In particular, the Levinson theorem and the generalized hypervirial theorem in higher dimensions, the Schrödinger equation with position-dependent mass and the Kaluza-Klein theory in higher dimensions are investigated. In this context, the dependence of the energy levels on the dimension is shown. Finally, Part V contains conclusions, outlooks and an extensive bibliography.

Keywords

High dimension quantum theory Higher dimensional quantum theory Kaluza-Klein theory high dimensions Levinson theorem Quantum theory relativity combine hypervirial theorem high dimensions quantum wave equation quantum wave equation high dimension quantum wave equation higher dimension quantum wave equations

Authors and affiliations

  • Shi-Hai Dong
    • 1
  1. 1.Escuela Superior de Física y Matemáticas, Unidad Profesional Adolfo López MateosInstituto Politécnico NacionalMexico D.F.Mexico

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-007-1917-0
  • Copyright Information Springer Science+Business Media B.V. 2011
  • Publisher Name Springer, Dordrecht
  • eBook Packages Physics and Astronomy
  • Print ISBN 978-94-007-1916-3
  • Online ISBN 978-94-007-1917-0
  • About this book
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