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An Introductory Path to Quantum Theory

Using Mathematics to Understand the Ideas of Physics

  • Textbook
  • © 2020

Overview

Authors:
  1. Stephen Bruce Sontz

    1. Matemáticas Básicas, Centro de Investigación en Matemáticas, A.C., Guanajuato, Mexico

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  • Introduction to quantum theory for students with some background in mathematics
  • Basic material can be covered in a one semester course
  • Aimed at advanced undergraduate and graduate students of mathematics, computer science, engineering and chemistry

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Table of contents (22 chapters)

  1. Front Matter

    Pages i-xxv
    Download chapter PDF

  2. Introduction to this Path

    • Stephen Bruce Sontz
    Pages 1-4

  3. Viewpoint

    • Stephen Bruce Sontz
    Pages 5-10

  4. Neither Particle nor Wave

    • Stephen Bruce Sontz
    Pages 11-16

  5. Schrödinger’s Equation

    • Stephen Bruce Sontz
    Pages 17-28

  6. Operators and Canonical Quantization

    • Stephen Bruce Sontz
    Pages 29-35

  7. The Harmonic Oscillator

    • Stephen Bruce Sontz
    Pages 37-46

  8. Interpreting \(\psi \): Mathematics

    • Stephen Bruce Sontz
    Pages 47-51

  9. Interpreting \(\psi \): Physics

    • Stephen Bruce Sontz
    Pages 53-60

  10. The Language of Hilbert Space

    • Stephen Bruce Sontz
    Pages 61-84

  11. Interpreting \(\psi \): Measurement

    • Stephen Bruce Sontz
    Pages 85-94

  12. The Hydrogen Atom

    • Stephen Bruce Sontz
    Pages 95-119

  13. Angular Momentum

    • Stephen Bruce Sontz
    Pages 121-131

  14. The Rotation Group SO(3)

    • Stephen Bruce Sontz
    Pages 133-148

  15. Spin and SU(2)

    • Stephen Bruce Sontz
    Pages 149-163

  16. Bosons and Fermions

    • Stephen Bruce Sontz
    Pages 165-167

  17. Classical and Quantum Probability

    • Stephen Bruce Sontz
    Pages 169-208

  18. The Heisenberg Picture

    • Stephen Bruce Sontz
    Pages 209-212

  19. Uncertainty (Optional)

    • Stephen Bruce Sontz
    Pages 213-227

  20. Speaking of Quantum Theory (Optional)

    • Stephen Bruce Sontz
    Pages 229-236
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Keywords

About this book

Since the 17th century, physical theories have been expressed in the language of mathematical equations. This introduction to quantum theory uses that language to enable the reader to comprehend the notoriously non-intuitive ideas of quantum physics. 

The mathematical knowledge needed for using this book comes from standard undergraduate mathematics courses and is described in detail in the section Prerequisites. This text is especially aimed at advanced undergraduate and graduate students of mathematics, computer science, engineering and chemistry among other disciplines, provided they have the math background even though lacking preparation in physics. In fact, no previous formal study of physics is assumed.




Reviews

“The target audience is ‘advanced undergraduate mathematics students who had no or only very little prior knowledge of physics’. It would indeed be a rare variety of mathematics advanced undergraduates who would fit this bill. … an interesting supplement for students with a mathematical bent.” (Amitava Raychaudhuri, zbMATH 1458.81002, 2021)

Authors and Affiliations

  • Matemáticas Básicas, Centro de Investigación en Matemáticas, A.C., Guanajuato, Mexico

    Stephen Bruce Sontz

About the author

Stephen Bruce Sontz received a Ph.D. from the University of Virginia with a dissertation in mathematical physics. He has published around 25 research articles in that field as well as two textbooks with Springer. These are "Quantum Principal Bundles, The Classical Case" and "Quantum Principal Bundles, The Quantum Case". He is a research professor at the Centro de Investigación en Matemáticas, A.C. (CIMAT) in Guanajuato, Mexico. He also teaches undergraduate courses in the Mathematics Department of the University of Guanajuato, where he has given courses using the material in this book. 

Bibliographic Information

  • Book Title: An Introductory Path to Quantum Theory

  • Book Subtitle: Using Mathematics to Understand the Ideas of Physics

  • Authors: Stephen Bruce Sontz

  • DOI: https://doi.org/10.1007/978-3-030-40767-4

  • Publisher: Springer Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer Nature Switzerland AG 2020

  • Hardcover ISBN: 978-3-030-40766-7Published: 17 March 2020

  • Softcover ISBN: 978-3-030-40769-8Published: 17 March 2021

  • eBook ISBN: 978-3-030-40767-4Published: 16 March 2020

  • Edition Number: 1

  • Number of Pages: XXV, 286

  • Number of Illustrations: 1 b/w illustrations

  • Topics: Mathematical Physics, Quantum Physics

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