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Quantum Mechanics in Matrix Form

  • Book
  • © 2018

Overview

Authors:
  1. Günter Ludyk

    1. Physics and Electrical Engineering, University of Bremen, Bremen, Germany

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  • Teaches how to numerically calculate quantum mechanics problems

  • Supports self study by numerous exercises

  • Explains how to map the higher-rank tensor operations of general relativity onto the more widely known two-dimensional matrix operations

  • Includes supplementary material: sn.pub/extras

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Table of contents (12 chapters)

  1. Front Matter

    Pages i-xiii
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  2. Quantum Theory Prior to 1925

    • Günter Ludyk
    Pages 1-9

  3. Heisenberg’s Year 1925

    • Günter Ludyk
    Pages 11-21

  4. Expansion of the Matrix Method

    • Günter Ludyk
    Pages 23-32

  5. Observables and Uncertainty Relations

    • Günter Ludyk
    Pages 33-46

  6. The Harmonic Oscillator

    • Günter Ludyk
    Pages 47-57

  7. Angular Momentum

    • Günter Ludyk
    Pages 59-75

  8. Wolfgang Pauli and the Hydrogen Atom

    • Günter Ludyk
    Pages 77-84

  9. Spin

    • Günter Ludyk
    Pages 85-104

  10. Atoms in Electromagnetic Fields

    • Günter Ludyk
    Pages 105-109

  11. Many Particle Systems

    • Günter Ludyk
    Pages 111-128

  12. Equivalence of Matrix and Wave Mechanics

    • Günter Ludyk
    Pages 129-140

  13. Relativistic Quantum Mechanics

    • Günter Ludyk
    Pages 141-154

  14. Back Matter

    Pages 155-214
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Keywords

About this book

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.

Authors and Affiliations

  • Physics and Electrical Engineering, University of Bremen, Bremen, Germany

    Günter Ludyk

About the author

After receiving his PhD in 1967, Günter Ludyk habilitated and has been appointed „Scientific Advisor and Professor“ (associate professor) of the Technical University of Berlin in 1970. In  1971 he has been a visiting professor at the Technical University of Graz/Austrial. Since 1972 he is a Full Professor at the Physics/Electrical Engineering Faculty of the University of Bremen. His area of research includes the theory of dynamical systems and the application of interval mathematics to generate high-precision results. He published various books on these topics both in German and English, e. g. "Time-Variant Discrete-Time-Systems” in 1981 and "Stability of Time-Variant Discrete-Time Systems” in 1985.

Bibliographic Information

  • Book Title: Quantum Mechanics in Matrix Form

  • Authors: Günter Ludyk

  • DOI: https://doi.org/10.1007/978-3-319-26366-3

  • Publisher: Springer Cham

  • eBook Packages: Physics and Astronomy, Physics and Astronomy (R0)

  • Copyright Information: Springer Nature Switzerland AG 2018

  • Hardcover ISBN: 978-3-319-26364-9Published: 03 November 2017

  • Softcover ISBN: 978-3-319-79941-4Published: 23 August 2018

  • eBook ISBN: 978-3-319-26366-3Published: 25 October 2017

  • Edition Number: 1

  • Number of Pages: XIII, 214

  • Number of Illustrations: 5 b/w illustrations, 9 illustrations in colour

  • Topics: Quantum Physics, Atomic/Molecular Structure and Spectra, Mathematical Methods in Physics

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