Factorization Method in Quantum Mechanics

  • Shi-Hai Dong

Part of the Fundamental Theories of Physics book series (FTPH, volume 150)

Table of contents

  1. Front Matter
    Pages I-XIX
  2. INTRODUCTION

    1. Front Matter
      Pages I-XIX
    2. Shi-Hai Dong
      Pages 3-12
  3. METHOD

    1. Front Matter
      Pages I-XIX
    2. Shi-Hai Dong
      Pages 15-16
    3. Shi-Hai Dong
      Pages 17-32
  4. APPLICATIONS IN NON-RELATIVISTIC QUANTUM MECHANICS

    1. Front Matter
      Pages I-XIX
    2. Shi-Hai Dong
      Pages 35-56
    3. Shi-Hai Dong
      Pages 57-71
    4. Shi-Hai Dong
      Pages 73-94
    5. Shi-Hai Dong
      Pages 95-110
    6. Shi-Hai Dong
      Pages 111-136
    7. Shi-Hai Dong
      Pages 143-149
    8. Shi-Hai Dong
      Pages 151-155
    9. Shi-Hai Dong
      Pages 157-168
    10. Shi-Hai Dong
      Pages 169-176
  5. APPLICATIONS IN RELATIVISTIC QUANTUM MECHANICS

About this book

Introduction

This Work introduces the factorization method in quantum mechanics at an advanced level with an aim to put mathematical and physical concepts and techniques like the factorization method, Lie algebras, matrix elements and quantum control at the Reader’s disposal. For this purpose a comprehensive description is provided of the factorization method and its wide applications in quantum mechanics which complements the traditional coverage found in the existing quantum mechanics textbooks. Related to this classic method are the supersymmetric quantum mechanics, shape invariant potentials and group theoretical approaches. It is no exaggeration to say that this method has become the milestone of these approaches. In fact the Author’s driving force has been his desire to provide a comprehensive review volume that includes some new and significant results about the factorization method in quantum mechanics since the literature is inundated with scattered articles in this field, and to pave the Reader’s way into this territory as rapidly as possible. The result: clear and understandable derivations with the necessary mathematical steps included so that the intelligent reader should be able to follow the text with relative ease, in particular when mathematically difficult material is presented.

Audience:
Researchers and students of physics, mathematics, chemistry and electrical engineering.

Keywords

Dirac equation Factorization method Harmonic and pseudoharmonic oscillators Laguerre functions algebras Shape invariant potential Supersymmetry

Authors and affiliations

  • Shi-Hai Dong
    • 1
  1. 1.Instituto Politécnico NacionalEscuela Superior de Física y MatemáticasMéxico

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4020-5796-0
  • Copyright Information Springer 2007
  • Publisher Name Springer, Dordrecht
  • eBook Packages Physics and Astronomy
  • Print ISBN 978-1-4020-5795-3
  • Online ISBN 978-1-4020-5796-0
  • About this book