Lectures on Quantum Mechanics
eBook - PDF

Lectures on Quantum Mechanics

A Primer for Mathematicians

  1. English
  2. PDF
  3. Available on iOS & Android
eBook - PDF

Lectures on Quantum Mechanics

A Primer for Mathematicians

About this book

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.

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Yes, you can access Lectures on Quantum Mechanics by Philip L. Bowers in PDF and/or ePUB format, as well as other popular books in Physical Sciences & Mathematical & Computational Physics. We have over one million books available in our catalogue for you to explore.

Table of contents

  1. Cover
  2. Half-title
  3. Title page
  4. Copyright information
  5. Contents
  6. Preface
  7. Prolegomenon
  8. 1 The Harmonic Oscillator: Classical versus Quantum
  9. 2 The Mathematical Structure of Quantum Mechanics
  10. 3 Observables and Expectation Values
  11. 4 The Projection Postulate Examined
  12. 5 Rigged Hilbert Space and the Dirac Calculus
  13. 6 A Review of Classical Mechanics
  14. 7 Hamilton–Jacobi Theory [star]
  15. 8 Classical Mechanics Regain’d
  16. 9 Wave Mechanics I: Heisenberg Uncertainty
  17. 10 Wave Mechanics II: The Fourier Transform
  18. 11 Wave Mechanics III: The Quantum Oscillator
  19. 12 Angular Momentum I: Basics
  20. 13 Angular Momentum II: Representations of su(2)
  21. 14 Angular Momentum III: The Central Force Problem
  22. 15 Wave Mechanics IV: The Hydrogenic Potential
  23. 16 Wave Mechanics V: Hidden Symmetry Revealed
  24. 17 Wave Mechanics VI: Hidden Symmetry Solved
  25. 18 Angular Momentum IV: Addition Rules and Spin
  26. 19 Wave Mechanics VII: Pauli’s Spinor Theory
  27. 20 Clifford Algebras and Spin Representations [star]
  28. 21 Many-Particle Quantum Systems
  29. 22 The EPR Argument and Bell’s Inequalities
  30. 23 Ensembles and Density Operators
  31. 24 Bosons and Fermions
  32. 25 The Fock Space for Indistinguishable Quanta
  33. 26 An Introduction to Quantum Statistical Mechanics
  34. 27 Quantum Dynamics
  35. 28 Unitary Representations and Conservation Laws
  36. 29 The Feynman Formulation of Quantum Mechanics
  37. 30 A Mathematical Interlude: Gaussian Integrals
  38. 31 Evaluating Path Integrals I
  39. 32 Evaluating Path Integrals II
  40. Epilogue
  41. Resources for Individual Exploration
  42. Bibliography
  43. Index