.

0 (hodnocen0 x )

BK

Second edition

Chichester : Wiley, A John Wiley and Sons, Ltd., Publication, [2009]

xvi, 671 stran : ilustrace ; 25 cm

ISBN 978-0-470-02679-3 (brožováno)

Obsahuje rejstřík

001640619

Preface to the Second Edition xiii // Preface to the First Edition xv // Note to the Student xvi // 1 Origins of Quantum Physics 1 // 1.1 Historical Note 1 // 1.2 Particle Aspect of Radiation 4 // 1.2.1 Blackbody Radiation 4 // 1.2.2 Photoelectric Effect 10 // 1.2.3 Compton Effect 13 // 1.2.4 Pair Production 16 // 1.3 Wave Aspect of Particles 18 // 1.3.1 de Broglie’s Hypothesis: Matter Waves 18 // 1.3.2 Experimental Confirmation of de Broglie’s Hypothesis 18 // 1.3.3 Matter Waves for Macroscopic Objects 20 // 1.4 Particles versus Waves 22 // 1.4.1 Classical View of Particles and Waves 22 // 1.4.2 Quantum View of Particles and Waves 23 // 1.4.3 Wave-Particle Duality: Complementarity 26 // 1.4.4 Principle of Linear Superposition 27 // 1.5 Indeterministic Nature of the Microphysical World 27 // 1.5.1 Heisenberg’s Uncertainty Principle 28 // 1.5.2 Probabilistic Interpretation 30 // 1.6 Atomic Transitions and Spectroscopy 30 // 1.6.1 Rutherford Planetary Model of the Atom 30 // 1.6.2 Bohr Model of the Hydrogen Atom 31 // 1.7 Quantization Rules 36 // 1.8 Wave Packets 38 // 1.8.1 Localized Wave Packets 39 // 1.8.2 Wave Packets and the Uncertainty Relations 42 // 1.8.3 Motion of Wave Packets 43 // 1.9 Concluding Remarks 54 // 1.10 Solved Problems 54 // 1.11 Exercises 71 // 2 Mathematical Tools of Quantum Mechanics 79 // 2.1 Introduction 79 // 2.2 The Hilbert Space and Wave Functions 79 // 2.2.1 The Linear Vector Space 79 // 2.2.2 The Hilbert Space 80 // 2.2.3 Dimension and Basis of a Vector Space 81 // 2.2.4 Square-lntegrable Functions: Wave Functions 84 // 2.3 Dirac Notation 84 // 2.4 Operators 89 // 2.4.1 General Definitions 89 // 2.4.2 Hermitian Adjoint 91 // 2.4.3 Projection Operators 92 // 2.4.4 Commutator Algebra 93 // 2.4.5 Uncertainty Relation between Two Operators 95 // 2.4.6 Functions of Operators 97 // 2.4.7 Inverse and Unitary Operators 98 //

2.4.8 Eigenvalues and Eigenvectors of an Operator 99 // 2.4.9 Infinitesimal and Finite Unitary Transformations 101 // 2.5 Representation in Discrete Bases 104 // 2.5.1 Matrix Representation of Kets, Bras, and Operators 105 // 2.5.2 Change of Bases and Unitary Transformations 114 // 2.5.3 Matrix Representation of the Eigenvalue Problem 117 // 2.6 Representation in Continuous Bases 121 // 2.6.1 General Treatment 121 // 2.6.2 Position Representation 123 // 2.6.3 Momentum Representation 124 // 2.6.4 Connecting the Position and Momentum Representations 124 // 2.6.5 Parity Operator 128 // 2.7 Matrix and Wave Mechanics 130 // 2.7.1 Matrix Mechanics 130 // 2.7.2 Wave Mechanics 131 // 2.8 Concluding Remarks 132 // 2.9 Solved Problems 133 // 2.10 Exercises 155 // 3 Postulates of Quantum Mechanics 165 // 3.1 Introduction 165 // 3.2 The Basic Postulates of Quantum Mechanics 165 // 3.3 The State of a System 167 // 3.3.1 Probability Density 167 // 3.3.2 The Superposition Principle 168 // 3.4 Observables and Operators 170 // 3.5 Measurement in Quantum Mechanics 172 // 3.5.1 How Measurements Disturb Systems 172 // 3.5.2 Expectation Values 173 // 3.5.3 Complete Sets of Commuting Operators (CSCO) 175 // 3.5.4 Measurement and the Uncertainty Relations 177 // 3.6 Time Evolution of the System’s State 178 // 3.6.1 Time Evolution Operator 178 // 3.6.2 Stationary States: Time-Independent Potentials 179 // 3.6.3 Schrödinger Equation and Wave Packets 180 // 3.6.4 The Conservation of Probability 181 // 3.6.5 Time Evolution of Expectation Values 182 // 3.7 Symmetries and Conservation Laws 183 // 3.7.1 Infinitesimal Unitary Transformations 184 // 3.7.2 Finite Unitary Transformations 185 // 3.7.3 Symmetries and Conservation Laws 185 // 3.8 Connecting Quantum to Classical Mechanics 187 // 3.8.1 Poisson Brackets and Commutators 187 // 3.8.2 The Ehrenfest Theorem 189 //

3.8.3 Quantum Mechanics and Classical Mechanics 190 // 3.9 Solved Problems 191 // 3.10 Exercises 209 // 4 One-Dimensional Problems 215 // 4.1 Introduction 215 // 4.2 Properties of One-Dimensional Motion 216 // 4.2.1 Discrete Spectrum (Bound States) 216 // 4.2.2 Continuous Spectrum (Unbound States) 217 // 4.2.3 Mixed Spectrum 217 // 4.2.4 Symmetric Potentials and Parity 218 // 4.3 The Free Particle: Continuous States 218 // 4.4 The Potential Step 220 // 4.5 The Potential Barrier and Well 224 // 4.5.1 The Case E > V0 224 // 4.5.2 The Case E < V0: Tunneling 227 // 4.5.3 The Tunneling Eifect 229 // 4.6 The Infinite Square Well Potential 231 // 4.6.1 The Asymmetric Square Well 231 // 4.6.2 The Symmetric Potential Well 234 // 4.7 The Finite Square Well Potential 234 // 4.7.1 The Scattering Solutions (E > V0) 235 // 4.7.2 The Bound State Solutions (Q < E < V0) 235 // 4.8 The Harmonic Oscillator 239 // 4.8.1 Energy Eigenvalues 241 // 4.8.2 Energy Eigenstates 243 // 4.8.3 Energy Eigenstates in Position Space 244 // 4.8.4 The Matrix Representation of Various Operators 247 // 4.8.5 Expectation Values of Various Operators 248 // 4.9 Numerical Solution of the Schrödinger Equation 249 // 4.9.1 Numerical Procedure 249 // 4.9.2 Algorithm 251 // 4.10 Solved Problems 252 // 4.11 Exercises 276 // 5 Angular Momentum // 5.1 Introduction // 5.2 Orbital Angular Momentum // 5.3 General Formalism of Angular Momentum // 5.4 Matrix Representation of Angular Momentum // 5.5 Geometrical Representation of Angular Momentum // 5.6 Spin Angular Momentum // 5.6.1 Experimental Evidence of the Spin // 5.6.2 General Theory of Spin // 5.6.3 Spin 1 /2 and the Pauli Matrices // 5.7 Eigenfunctions of Orbital Angular Momentum // 5.7.1 Eigenfunctions and Eigenvalues of Lz // 5.7.2 Eigenfunctions of L2 // 5.7.3 Properties of the Spherical Harmonics // 5.8 Solved Problems // 5.9 Exercises //

6 Three-Dimensional Problems // 6.1 Introduction // 6.2 3D Problems in Cartesian Coordinates // 6.2.1 General Treatment: Separation of Variables // 6.2.2 The Free Particle // 6.2.3 The Box Potential // 6.2.4 The Harmonic Oscillator // 6.3 3D Problems in Spherical Coordinates // 6.3.1 Central Potential: General Treatment // 6.3.2 The Free Particle in Spherical Coordinates // 6.3.3 The Spherical Square Well Potential // 6.3.4 The Isotropic Hannonic Oscillator // 6.3.5 The Hydrogen Atom // 6.3.6 Effect of Magnetic Fields on Central Potentials // 6.4 Concluding Remarks // 6.5 Solved Problems // 6.6 Exercises // 7 Rotations and Addition of Angular Momenta // 7.1 Rotations in Classical Physics // 7.2 Rotations in Quantum Mechanics // 7.2.1 Infinitesimal Rotations // 7.2.2 Finite Rotations // 7.2.3 Properties of the Rotation Operator // 7.2.4 Euler Rotations // 7.2.5 Representation of the Rotation Operator // 7.2.6 Rotation Matrices and the Spherical Harmonics // 7.3 Addition of Angular Momenta // 7.3.1 Addition of Two Angular Momenta: General Formalism . // 7.3.2 Calculation of the Clebsch-Gordan Coefficients // 7.3.3 Coupling of Orbital and Spin Angular Momenta 415 // 7.3.4 Addition of More Than Two Angular Momenta 419 // 7.3.5 Rotation Matrices for Coupling Two Angular Momenta 420 // 7.3.6 Isospin 422 // 7.4 Scalar, Vector, and Tensor Operators 425 // 7.4.1 Scalar Operators // 7.4.2 Vector Operators 426 // 7.4.3 Tensor Operators: Reducible and Irreducible Tensors 428 // 7.4.4 Wigner-Eckart Theorem for Spherical Tensor Operators 430 // 7.5 Solved Problems 434 // 7.6 Exercises 430 // 8 Identical Particles 455 // 8.1 Many-Particle Systems 455 // 8.1.1 Schrödinger Equation // 8.1.2 Interchange Symmetry // 8.1.3 Systems of Distinguishable Noninteracting Particles 458 // 8.2 Systems of Identical Particles 460 // 8.2.1 Identical Particles in Classical and Quantum Mechanics 460 //

8.2.2 Exchange Degeneracy 462 // 8.2.3 Symmetrization Postulate 463 // 8.2.4 Constructing Symmetric and Antisymmetric Functions 464 // 8.2.5 Systems of Identical Noninteracting Particles 464 // 8.3 The Pauli Exclusion Principle 467 // 8.4 The Exclusion Principle and the Periodic Table 469 // 8.5 Solved Problems 473 // 8.6 Exercises 484 // 9 Approximation Methods for Stationary States 489 // 9.1 Introduction 489 // 9.2 Time-Independent Perturbation Theory 490 // 9.2.1 Nondegenerate Perturbation Theory 490 // 9.2.2 Degenerate Perturbation Theory 496 // 9.2.3 Fine Structure and the Anomalous Zeeman Effect 499 // 9.3 The Variational Method 5Q7 // 9.4 The Wentzel-Kramers-Brillouin Method 515 // 9.4.1 General Formalism // 9.4.2 Bound States for Potential Wells with No Rigid Walls 518 // 9.4.3 Bound States for Potential Wells with One Rigid Wall 524 // 9.4.4 Bound States for Potential Wells with Two Rigid Walls 525 // 9.4.5 Tunneling through a Potential Barrier 528 // 9.5 Concluding Remarks 53? // 9.6 Solved Problems 53? // 9.7 Exercises // 10 Time-Dependent Perturbation Theory 571 // 10.1 Introduction // 10.2 The Pictures of Quantum Mechanics 571 // 10.2.1 The Schrödinger Picture 572 // 10.2.2 The Heisenberg Picture 572 // 10.2.3 The Interaction Picture 573 // 10.3 Time-Dependent Perturbation Theory 574 // 10.3.1 Transition Probability 575 // 10.3.2 Transition Probability for a Constant Perturbation 577 // 10.3.3 Transition Probability for a Harmonic Perturbation 579 // 10.4 Adiabatic and Sudden Approximations 582 // 10.4.1 Adiabatic Approximation 532 // 10.4.2 Sudden Approximation 533 // 10.5 Interaction of Atoms with Radiation 586 // 10.5.1 Classical Treatment of the Incident Radiation 587 // 10.5.2 Quantization of the Electromagnetic Field 588 // 10.5.3 Transition Rates for Absorption and Emission of Radiation 591 // 10.5.4 Transition Rates within the Dipole Approximation 592 //

10.5.5 The Electric Dipole Selection Rules 593 // 10.5.6 Spontaneous Emission 594 // 10.6 Solved Problems // 10.7 Exercises 613 // 11 Scattering Theory 617 // 11.1 Scattering and Cross Section 617 // 11.1.1 Connecting the Angles in the Lab and CM frames 618 // 11.1.2 Connecting the Lab and CM Cross Sections 620 // 11.2 Scattering Amplitude of Spinless Particles 621 // 11.2.1 Scattering Amplitude and Differential Cross Section 623 // 11.2.2 Scattering Amplitude 624 // 11.3 The Born Approximation 628 // 11.3.1 The First Born Approximation 628 // 11.3.2 Validity of the First Bom Approximation 629 // 11.4 Partial Wave Analysis 631 // 11.4.1 Partial Wave Analysis for Elastic Scattering 631 // 11.4.2 Partial Wave Analysis for Inelastic Scattering 635 // 11.5 Scattering of Identical Particles 636 // 11.6 Solved Problems 639 // 11.7 Exercises 650 // A The Delta Function 653 // A.l One-Dimensional Delta Function 653 // A. 1.1 Various Definitions of the Delta Function 653 // A. 1.2 Properties of the Delta Function 654 // A. 1.3 Derivative of the Delta Function 655 // A.2 Three-Dimensional Delta Function 656 // B Angular Momentum in Spherical Coordinates 657 // B.1 Derivation of Some General Relations 657 // B.2 Gradient and Laplacian in Spherical Coordinates 658 // B.3 Angular Momentum in Spherical Coordinates 659 // C C++ Code for Solving the Schrödinger Equation 661 // Index 665

(OCoLC)255894625