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Lectures on Quantum Mechanics

Lectures on Quantum Mechanics
A Primer for Mathematicians

  • Publication planned for: July 2020
  • availability: Not yet published - available from July 2020
  • format: Hardback
  • isbn: 9781108429764

Hardback

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  • Quantum mechanics is one of the principle pillars of modern physics. It also remains a topic of great interest to mathematicians. Since its discovery it has inspired and been inspired by many topics within modern mathematics, including functional analysis and operator algebras, Lie groups, Lie algebras and their representations, principle bundles, distribution theory, and much more. Written with beginning graduate students in mathematics in mind, this book provides a thorough treatment of (nonrelativistic) quantum mechanics in a style that is leisurely, without the usual theorem-proof grammar of pure mathematics, while remaining mathematically honest. The author takes the time to fully develop the required mathematics and employs a consistent mathematical presentation to clarify the often-confusing notation of physics texts. Along the way the reader encounters several topics requiring more advanced mathematics than found in many discussions of the subject, making for a fascinating course in how mathematics and physics interact.

    • A mathematically honest treatment of quantum mechanics suitable for graduate students
    • Develops the required mathematics in full while retaining a leisurely style
    • Features several topics of interest requiring more advanced mathematics than found in many quantum mechanics texts
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    Product details

    • Publication planned for: July 2020
    • format: Hardback
    • isbn: 9781108429764
    • dimensions: 228 x 152 mm
    • availability: Not yet published - available from July 2020
  • Table of Contents

    Preface (in five short acts)
    Prolegomenon
    Part I Nonrelativistic Quantum Mechanics
    1. The Harmonic Oscillator: Classical verses Quantum
    2. The Mathematical Structure of Quantum Mechanics
    3. Observables: Self-adjoint Operators and Expectation Values
    4. The Projection Postulate Examined
    5. Rigged Hilbert Space and the Dirac Calculus
    6. A Review of Classical Mechanics
    7. Hamilton-Jacobi Theory *
    8. Classical Mechanics Regain'd
    9. Wave Mechanics I: The Heisenberg Uncertainty Principle
    10. Wave Mechanics II: The Fourier Transform
    11. Wave Mechanics III: The Quantum Oscillator
    12. Angular Momentum Operators I: Basics
    13. Angular Momentum Operators II: Representations of su(2)
    14. Angular Momentum Operators III: The Central Force Problem
    15. Wave Mechanics IV: The Hydrogenic Potential
    16. Wave Mechanics V: Hidden Symmetry
    17. Wave Mechanics VI: Representations and Group Characters
    18. Angular Momentum Operators IV: Addition Rules, etc.
    19. Wave Mechanics VII: Pauli's Spinor Theory
    20. Cli ord Algebras and Spin Representations *
    21. Many Particle Quantum Systems
    22. The EPR Argument, Nonlocality, and Bell's Inequalities
    23. Ensembles and Density Operators
    24. Bosons and Fermions
    25. The Fock Space for Indistinguishable Quanta
    26. A Brief Introduction to Quantum Statistical Mechanics
    27. Quantum Dynamics
    28. Unitary Representations, Symmetry, and Conservation Laws
    29. The Feynman Formulation of Quantum Mechanics
    30. A Mathematical Interlude: Gaussian Integrals
    31. Evaluating Path Integrals I
    32. Evaluating Path Integrals II
    References
    Epilogue
    Resources for Individual Exploration
    Bibliography
    Index.

  • Author

    Philip L. Bowers, Florida State University
    Philip L Bowers is the Dwight B. Goodner Professor of Mathematics at Florida State University.

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