A Mathematical Primer on Quantum Mechanics

  • Alessandro Teta

Part of the UNITEXT for Physics book series (UNITEXTPH)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Alessandro Teta
    Pages 45-59
  3. Alessandro Teta
    Pages 61-77
  4. Alessandro Teta
    Pages 79-122
  5. Alessandro Teta
    Pages 123-138
  6. Alessandro Teta
    Pages 139-158
  7. Alessandro Teta
    Pages 159-174
  8. Alessandro Teta
    Pages 175-202
  9. Alessandro Teta
    Pages 203-233
  10. Back Matter
    Pages 235-259

About this book

Introduction

This book offers a rigorous yet elementary approach to quantum mechanics that will meet the needs of Master’s-level Mathematics students and is equally suitable for Physics students who are interested in gaining a deeper understanding of the mathematical structure of the theory. Throughout the coverage, which is limited to single-particle quantum mechanics, the focus is on formulating theory and developing applications in a mathematically precise manner.

Following a review of selected key concepts in classical physics and the historical background, the basic elements of the theory of operators in Hilbert spaces are presented and used to formulate the rules of quantum mechanics. The discussion then turns to free particles, harmonic oscillators, delta potential, and hydrogen atoms, providing rigorous proofs of the corresponding dynamical properties. Starting from an analysis of these applications, readers are subsequently introduced to more advanced topics such as the classical limit, scattering theory, and spectral analysis of Schrödinger operators. The main content is complemented by numerous exercises that stimulate interactive learning and help readers check their progress.

 

Keywords

Quantum mechanics textbook for mathematicians Mathematical physics textbook Dynamics of a quantum particle Solvable models in quantum mechanics Operators in Hilbert spaces elementary theory of Hilbert spaces scattering theory for mathematicians

Authors and affiliations

  • Alessandro Teta
    • 1
  1. 1.Dipartimento di Matematica Guido CastelnuovoUniversità degli Studi di Roma “La Sapienza”RomeItaly

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-77893-8
  • Copyright Information Springer International Publishing AG, part of Springer Nature 2018
  • Publisher Name Springer, Cham
  • eBook Packages Physics and Astronomy
  • Print ISBN 978-3-319-77892-1
  • Online ISBN 978-3-319-77893-8
  • Series Print ISSN 2198-7882
  • Series Online ISSN 2198-7890
  • About this book
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