Quantum Mechanics in Matrix Form

  • Günter Ludyk

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Günter Ludyk
    Pages 1-9
  3. Günter Ludyk
    Pages 11-21
  4. Günter Ludyk
    Pages 23-32
  5. Günter Ludyk
    Pages 33-46
  6. Günter Ludyk
    Pages 47-57
  7. Günter Ludyk
    Pages 59-75
  8. Günter Ludyk
    Pages 77-84
  9. Günter Ludyk
    Pages 85-104
  10. Günter Ludyk
    Pages 105-109
  11. Günter Ludyk
    Pages 111-128
  12. Günter Ludyk
    Pages 129-140
  13. Günter Ludyk
    Pages 141-154
  14. Back Matter
    Pages 155-214

About this book

Introduction

This book gives an introduction to quantum mechanics with the matrix method. Heisenberg's matrix mechanics is described in detail. The fundamental equations are derived by algebraic methods using matrix calculus. Only a brief description of Schrödinger's wave mechanics is given (in most books exclusively treated), to show their equivalence to Heisenberg's matrix  method. In the first part the historical development of Quantum theory by Planck, Bohr and Sommerfeld is sketched, followed by the ideas and methods of Heisenberg, Born and Jordan. Then Pauli's spin and exclusion principles are treated. Pauli's exclusion principle leads to the structure of atoms. Finally, Dirac´s relativistic quantum mechanics is shortly presented. Matrices and matrix equations are today easy to handle when implementing numerical algorithms using standard software as MAPLE and Mathematica.

Keywords

Axiomatic Description of Square Matrix Bohr-Sommerfeld Quantization Rule Eigenvalues and Eigenvectors Equivalence of Matrix with Wave Mechanics Expansion of the Matrices Method Kronecker Product Matrix Vector of Angular Momentum Permutation Matrix Projection Matrices Schur product of matrices 173

Authors and affiliations

  • Günter Ludyk
    • 1
  1. 1.Physics and Electrical EngineeringUniversity of BremenBremenGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-26366-3
  • Copyright Information Springer International Publishing AG 2018
  • Publisher Name Springer, Cham
  • eBook Packages Physics and Astronomy
  • Print ISBN 978-3-319-26364-9
  • Online ISBN 978-3-319-26366-3
  • About this book