Quantum. Mechanics. Y y. A Modern Development. 2nd Edition. Leslie E Ballentine. World Scientific. Simon Fraser University, Canada TAIPEI BEIJING

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1 BEIJING TAIPEI Quantum Mechanics A Modern Development 2nd Edition Leslie E Ballentine Simon Fraser University, Canada Y y NEW JERSEY LONDON SINGAPORE World Scientific SHANGHAI HONG KONG CHENNAI

2 Contents Preface XI Introduction: The Phenomena of Quantum Mechanics 1 Chapter 1 Mathematical Prerequisites 7 11 Linear Vector Space 7 12 Linear Operators Self-Adjoint Operators Hilbert Space and Rigged Hilbert Space Probability Theory 29 Problems 38 Chapter 2 The Formulation of Quantum Mechanics Basic Theoretical Concepts Conditions on Operators General States and Pure States Probability Distributions 55 Problems 60 Chapter 3 Kinematics and Dynamics Transformations of States and Observables The Symmetries of Space-Time Generators of the Galilei Group Identification of Operators with Dynamical Variables Composite Systems [[Quantizing a Classical System]] Equations of Motion Symmetries and Conservation Laws 92 Problems 94 V

3 vj CoiiteJils Chapter 4 Coordinate Representation and Applications Coordinate Representation The Wave Equation and Its Interpretation Galilei Transformation of Schrodinger's Equation Probability Flux Conditions on Wave Functions Energy Eigenfunctions for Free Particles Tunneling Path Integrals 116 Problems 123 Chapter 5 Momentum Representation and Applications Momentum Representation Momentum Distribution in an Atom Bloch's Theorem Diffraction Scattering: Theory Diffraction Scattering: Experiment Motion in a Uniform Force Field 145 Problems 149 Chapter 6 The Harmonic Oscillator Algebraic Solution Solution in Coordinate Representation Solution in H Representation 157 Problems 158 Chapter 7 Angular Momemtum Eigenvalues and Matrix Elements Explicit Form of the Angular Momentum Operators Orbital Angular Momentum Spin Finite Rotations Rotation Through 2?r Addition of Angular Momenta Irreducible Tensor Operators Rotational Motion of a Rigid Body 200 Problems 203

4 Contents vii Chapter 8 State Preparation and Determination State Preparation State Determination States of Composite Systems 2 Hi 84 Indeterminacy Relations 223 Problems 227 Chapter 9 Measurement and the Interpretation of States An Example of Spin Measurement A General Theorem of Measurement Theory The Interpretation of a State Vector Which Wave Function? Spin Recombination Experiment Joint and Conditional Probabilities 244 Problems 254 Chapter 10 Formation of Bound States Spherical Potential Well The Hydrogen Atom Estimates from Indeterminacy Relations Some Unusual Bound States Stationary State Perturbation Theory 27G 106 Variational Method 290 Problems 304 Chapter 11 Charged Particle in a Magnetic Field Classical Theory Quantum Theory Motion in a Uniform Static Magnetic Field The Aharonov Bohm Effect The Zeeman Effect 325 Problems 330 Chapter 12 Time-Dependent Phenomena Spin Dynamics Exponential and Nonexponenlial Decay Energy Time Indeterminacy Relations Quantum Beats Time-Dependent Perturbation Theory 349

5 126 Atomic Radiation Adiabatic Approximation 363 Problems 367 Chapter 13 Discrete Symmetries Space Inversion Parity Nonconservation Time Reversal 377 Problems 386 Chapter 14 The Classical Limit Ehrenfest's Theorem and Beyond The Hamilton-Jacobi Equation and the Quantum Potential Quantal Trajectories The Large Quantum Number Limit 400 Problems 404 Chapter 15 Quantum Mechanics in Phase Space Why Phase Space Distributions? The Wigner Representation The Husimi Distribution 414 Problems 420 Chapter 16 Scattering Cross Section Scattering by a Spherical Potential General Scattering Theory Born Approximation and DWBA Scattering Operators Scattering Resonances Diverse Topics 462 Problems 468 Chapter 17 Identical Particles Permutation Symmetry Indistinguishability of Particles ' The Symmctrization Postulate Creation and Annihilation Operators 478

6 Contents ix Problems -102 Chapter 18 Many-Fermion Systems Exchange The Hartree -Fock Method Dynamic Correlations Fundamental Consequences for Theory BCS Pairing Theory 514 Problems 525 Chapter 19 Quantum Mechanics of the Electromagnetic Field Normal Modes of the Field 52G 192 Electric and Magnetic Field Operators Zero-Point Energy and the Casimir Force States of the EM Field Spontaneous Emission Photon Detectors Correlation Functions Coherence Optical Homodyne Tomography Determining the Quantum State of the Field 578 Problems Chapter 20 Bell's Theorem and Its Consequences The Argument of Einstein, Podolsky, and Rosen 202 Spin Correlations Bell's Inequality A Stronger Proof of Bell's Theorem Polarization Correlations Bell's Theorem Without Probabilities Implications of Bell's Theorem 607 Problems 611 Chapter 21 Quantum Information Quantum States as Carriers of Information Some Quantum Information Theorems Quantum Transmission of Information Cryptography 626

7 x Contents 215 Entanglement Teleportation of Quantum States Quantum Information from Independent Pairs Measurable 'In Principle" Quantum Computing Quantum Information and Quantum Foundations 661 Problems 671 Appendix A Schur's Lemma 673 Appendix B Irreducibility of Q and P 675 Appendix C Proof of Wick's Theorem 676 Appendix D Solutions to Selected Problems 678 Bibliography 699 Index 715

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