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Quantum Mechanics

Book Description

The important changes quantum mechanics has undergone in recent years are reflected in this new approach for students. A strong narrative, and over 300 worked problems lead the student from experiment, through general principles of the theory, to modern applications. Stepping through results allows students to gain a thorough understanding. Starting with basic quantum mechanics, the book moves on to more advanced theory, followed by applications, perturbation methods and special fields, and ending with new developments in the field. Historical, mathematical, and philosophical boxes guide the student through the theory. Unique to this textbook are chapters on measurement and quantum optics, both at the forefront of current research. Advanced undergraduate and graduate students will benefit from this new perspective on the fundamental physical paradigm and its applications. Online resources including solutions to selected problems, and 200 figures, with colour versions of some figures, are available at www.cambridge.org/9780521869638.

Table of Contents

  1. Cover
  2. Half Title
  3. Title Page
  4. Copyright
  5. Contents
  6. List of figures
  7. List of tables
  8. List of definitions, principles, etc.
  9. List of boxes
  10. List of symbols
  11. List of abbreviations
  12. Acknowledgements for the revised edition
  13. Introduction
  14. Part I: Basic features of quantum mechanics
    1. 1. From classical mechanics to quantum mechanics
      1. 1.1 Review of the foundations of classical mechanics
      2. 1.2 An interferometry experiment and its consequences
      3. 1.3 State as vector
      4. 1.4 Quantum probability
      5. 1.5 The historical need of a new mechanics
      6. Summary
      7. Problems
      8. Further reading
    2. 2. Quantum observables and states
      1. 2.1 Basic features of quantum observables
      2. 2.2 Wave function and basic observables
      3. 2.3 Uncertainty relation
      4. 2.4 Quantum algebra and quantum logic
      5. Summary
      6. Problems
      7. Further reading
    3. 3. Quantum dynamics
      1. 3.1 The Schrödinger equation
      2. 3.2 Properties of the Schrödinger equation
      3. 3.3 Schrödinger equation and Galilei transformations
      4. 3.4 One-dimensional free particle in a box
      5. 3.5 Unitary transformations
      6. 3.6 Different pictures
      7. 3.7 Time derivatives and the Ehrenfest theorem
      8. 3.8 Energy–time uncertainty relation
      9. 3.9 Towards a time operator
      10. Summary
      11. Problems
      12. Further reading
    4. 4. Examples of quantum dynamics
      1. 4.1 Finite potential wells
      2. 4.2 Potential barrier
      3. 4.3 Tunneling
      4. 4.4 Harmonic oscillator
      5. 4.5 Quantum particles in simple fields
      6. Summary
      7. Problems
    5. 5. Density matrix
      1. 5.1 Basic formalism
      2. 5.2 Expectation values and measurement outcomes
      3. 5.3 Time evolution and density matrix
      4. 5.4 Statistical properties of quantum mechanics
      5. 5.5 Compound systems
      6. 5.6 Pure- and mixed-state representation
      7. Summary
      8. Problems
      9. Further reading
  15. Part II: More advanced topics
    1. 6. Angular momentum and spin
      1. 6.1 Orbital angular momentum
      2. 6.2 Special examples
      3. 6.3 Spin
      4. 6.4 Composition of angular momenta and total angular momentum
      5. 6.5 Angular momentum and angle
      6. Summary
      7. Problems
      8. Further reading
    2. 7. Identical particles
      1. 7.1 Statistics and quantum mechanics
      2. 7.2 Wave function and symmetry
      3. 7.3 Spin and statistics
      4. 7.4 Exchange interaction
      5. 7.5 Two recent applications
      6. Summary
      7. Problems
      8. Further reading
    3. 8. Symmetries and conservation laws
      1. 8.1 Quantum transformations and symmetries
      2. 8.2 Continuous symmetries
      3. 8.3 Discrete symmetries
      4. 8.4 A brief introduction to group theory
      5. Summary
      6. Problems
      7. Further reading
    4. 9. The measurement problem in quantum mechanics
      1. 9.1 Statement of the problem
      2. 9.2 A brief history of the problem
      3. 9.3 Schrödinger cats
      4. 9.4 Decoherence
      5. 9.5 Reversibility/irreversibility
      6. 9.6 Interaction-free measurement
      7. 9.7 Delayed-choice experiments
      8. 9.8 Quantum Zeno effect
      9. 9.9 Conditional measurements or postselection
      10. 9.10 Positive operator valued measure
      11. 9.11 Quantum non-demolition measurements
      12. 9.12 Decision and estimation theory
      13. Summary
      14. Problems
      15. Further reading
  16. Part III: Matter and light
    1. 10. Perturbations and approximation methods
      1. 10.1 Stationary perturbation theory
      2. 10.2 Time-dependent perturbation theory
      3. 10.3 Adiabatic theorem
      4. 10.4 The variational method
      5. 10.5 Classical limit
      6. 10.6 Semiclassical limit and WKB approximation
      7. 10.7 Scattering theory
      8. 10.8 Path integrals
      9. Summary
      10. Problems
      11. Further reading
    2. 11. Hydrogen and helium atoms
      1. 11.1 Introduction
      2. 11.2 Quantum theory of the hydrogen atom
      3. 11.3 Atom and magnetic field
      4. 11.4 Relativistic corrections
      5. 11.5 Helium atom
      6. 11.6 Many-electron effects
      7. Summary
      8. Problems
      9. Further reading
    3. 12. Hydrogen molecular ion
      1. 12.1 The molecular problem
      2. 12.2 Born–Oppenheimer approximation
      3. 12.3 Vibrational and rotational degrees of freedom
      4. 12.4 The Morse potential
      5. 12.5 Chemical bonds and further approximations
      6. Summary
      7. Problems
      8. Further reading
    4. 13. Quantum optics
      1. 13.1 Quantization of the electromagnetic field
      2. 13.2 Thermodynamic equilibrium of the radiation field
      3. 13.3 Phase–number uncertainty relation
      4. 13.4 Special states of the electromagnetic field
      5. 13.5 Quasi-probability distributions
      6. 13.6 Quantum-optical coherence
      7. 13.7 Atom–field interaction
      8. 13.8 Geometric phase
      9. 13.9 The Casimir effect
      10. Summary
      11. Problems
      12. Further reading
  17. Part IV: Quantum information: state and correlations
    1. 14. Quantum theory of open systems
      1. 14.1 General considerations
      2. 14.2 The master equation
      3. 14.3 A formal generalization
      4. 14.4 Quantum jumps and quantum trajectories
      5. 14.5 Quantum optics and Schrödinger cats
      6. Summary
      7. Problems
      8. Further reading
    2. 15. State measurement in quantum mechanics
      1. 15.1 Protective measurement of the state
      2. 15.2 Quantum cloning and unitarity violation
      3. 15.3 Measurement and reversibility
      4. 15.4 Quantum state reconstruction
      5. 15.5 The nature of quantum states
      6. Summary
      7. Problems
      8. Further reading
    3. 16. Entanglement: non-separability
      1. 16.1 EPR
      2. 16.2 Bohm’s version of the EPR state
      3. 16.3 HV theories
      4. 16.4 Bell’s contribution
      5. 16.5 Experimental tests
      6. 16.6 Bell inequalities with homodyne detection
      7. 16.7 Bell theorem without inequalities
      8. 16.8 What is quantum non-locality?
      9. 16.9 Further developments about inequalities
      10. 16.10 Conclusion
      11. Summary
      12. Problems
      13. Further reading
    4. 17. Entanglement: quantum information and computation
      1. 17.1 Information and entropy
      2. 17.2 Entanglement and information
      3. 17.3 Measurement and information
      4. 17.4 Qubits
      5. 17.5 Teleportation
      6. 17.6 Quantum cryptography
      7. 17.7 Elements of quantum computation
      8. 17.8 Quantum algorithms and error correction
      9. Summary
      10. Problems
      11. Further reading
  18. Bibliography
  19. Author index
  20. Subject index