Hilbert Spaces, Wavelets, Generalised Functions and Modern Quantum Mechanics

Overview

This book gives a comprehensive introduction to modern quantum mechanics, emphasising the underlying Hilbert space theory and generalised function theory. All the major modern techniques and approaches used in quantum mechanics are introduced, such as Berry phase, coherent and squeezed states, quantum computing, solitons and quantum mechanics.
Audience: The book is suitable for graduate students in physics and mathematics.
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Paperback (Softcover reprint of the original 1st ed. 1998)
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Overview

This book gives a comprehensive introduction to modern quantum mechanics, emphasising the underlying Hilbert space theory and generalised function theory. All the major modern techniques and approaches used in quantum mechanics are introduced, such as Berry phase, coherent and squeezed states, quantum computing, solitons and quantum mechanics.
Audience: The book is suitable for graduate students in physics and mathematics.
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Editorial Reviews

Booknews
This textbook gives an introduction to Hilbert space theory, Fourier transform and wavelets, linear operators, generalized functions, and quantum mechanics. The first four chapters give an introduction to the mathematical tools necessary in quantum mechanics. The remaining chapters are devoted to quantum mechanics, and the final chapter introduces Lebesgue integration theory. All the major modern techniques and approaches used in quantum mechanics are introduced, including Berry phase, coherent and squeezed states, quantum computing, solitons, and quantum mechanics. Suitable for graduate students in physics and mathematics. Annotation c. by Book News, Inc., Portland, Or.
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Product Details

  • ISBN-13: 9789401062411
  • Publisher: Springer Netherlands
  • Publication date: 12/31/2013
  • Series: Mathematics and Its Applications (closed) Series
  • Edition description: Softcover reprint of the original 1st ed. 1998
  • Pages: 238
  • Product dimensions: 6.14 (w) x 9.21 (h) x 0.53 (d)

Table of Contents

List of Symbols. Preface. 1. Hilbert Spaces. 2. Fourier Transform and Wavelets. 3. Linear Operators in Hilbert Spaces. 4. Generalized Functions. 5. Classical Mechanics and Hamilton Systems. 6. Postulates of Quantum Mechanics. 7. Interaction Picture. 8. Eigenvalue Problem. 9. Spin Matrices and Kronecker Product. 10. Parity and Group Theory. 11. Uncertainty Relation. 12. Harmonic Oscillator. 13. Coherent and Squeezed States. 14. Angular Momentum and Lie Algebras. 15. Two-Body Bound State Problem. 16. One-Dimensional Scattering. 17. Solitons and Quantum Mechanics. 18. Perturbation Theory. 19. Helium Atom. 20. Potential Scattering. 21. Berry Phase. 12. Measurement and Quantum States. 13. Quantum Computing. 24. Lebesgue Integration and Stieltjes Integral. Bibliography. Index.
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