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BK

Third edition

Hoboken : Wiley, 2022

xx, 1001 stran : ilustrace ; 25 cm

ISBN 978-1-118-30789-2 (brožováno)

Obsahuje bibliografické odkazy a rejstřík

001658084

1 Origins of Quantum Physics 1 // 1.1 Historical Note: From Classical to Modem Physics 1 // 1.1.1 1859-1900: Failure of Classical Physics at the Microscopic Scale 2 // 1.1.2 1900-1932: Advent of Quantum Mechanics - New Era in Physics 4 // 1.2 Particle Aspect of Radiation 12 // 1.2.1 Blackbody Radiation 13 // 1.2.2 Photoelectric Effect 19 // 1.2.3 Compton Effect 23 // 1.2.4 Pair Production 25 // 1.3 Wave Aspect of Particles 27 // 1.3.1 de Broglie’s Hypothesis: Matter Waves 27 // 1.3.2 Experimental Confirmation of de Broglie’s Hypothesis 28 // 1.3.3 Matter Waves for Macroscopic Objects 30 // 1.4 Particles versus Waves 31 // 1.4.1 Classical View of Particles and Waves 31 // 1.4.2 Quantum View of Particles and Waves 33 // 1.4.3 Wave-Particle Duality: Complementarity 35 // 1.4.4 Principle of Linear Superposition 37 // 1.5 Indeterministic Nature of the Microphysical World 38 // 1.5.1 Heisenberg’s Uncertainty Principle 38 // 1.5.2 Probabilistic Interpretation 40 // 1.6 Bohr’s Atomic Model, Atomic Transitions and Spectroscopy 40 // 1.6.1 Rutherford Planetary Model of the Atom 41 // 1.6.2 Bohr Model of the Hydrogen Atom 41 // 1.7 Quantization Rules 48 // 1.8 Wave Packets 50 // 1.8.1 Localized Wave Packets 51 // 1.8.2 Wave Packets and the Uncertainty Relations 54 // 1.8.3 Motion of Wave Packets 55 // 1.9 Concluding Remarks 66 // 1.10 Solved Problems 67 // 1.11 Exercises 84 // 2 Mathematical Tools of Quantum Mechanics 91 // 2.1 Introduction 91 // 2.2 The Hilbert Space and Wave Functions 91 // 2.2.1 The Linear Vector Space 91 // 2.2.2 The Hilbert Space 92 // 2.2.3 Dimension and Basis of a Vector Space 93 // 2.2.4 Square-Integrable Functions: Wave Functions 96 // 2.3 Dirac Notation 97 // 2.4 Operators 104 // 2.4.1 General Definitions 104 // 2.4.2 Hermitian Adjoint 105 // 2.4.3 Projection Operators 107 // 2.4.4 Commutator Algebra 108 // 2.4.5 Uncertainty Relation between Two Operators 110 //

2.4.6 Functions of Operators 112 // 2.4.7 Inverse of an Operator and Unitary Operators 113 // 2.4.8 Antilinear and Antiunitary Operators, Wigner Theorem 114 // 2.4.9 Eigenvalues and Eigenvectors of an Operator 118 // 2.4.10 Infinitesimal and Finite Unitary Transformations 120 // 2.5 Representation in Discrete Bases 123 // 2.5.1 Matrix Representation of Kets, Bras, and Operators 123 // 2.5.2 Change of Bases and Unitary Transformations 134 // 2.5.3 Matrix Representation of the Eigenvalue Problem 137 // 2.6 Representation in Continuous Bases 141 // 2.6.1 General Treatment 141 // 2.6.2 Position Representation 142 // 2.6.3 Momentum Representation 143 // 2.6.4 Connecting the Position and Momentum Representations 144 // , 2.6.5 Parity Operator 148 // 2.7 Matrix and Wave Mechanics 150 // 2.7.1 Matrix Mechanics 151 // 2.7.2 Wave Mechanics 151 // 2.8 Concluding Remarks 152 // 2.9 Solved Problems 153 // 2.10 Exercises 176 // 3 Postulates of Quantum Mechanics 187 // 3.1 Introduction 187 // 3.2 The Basic Postulates of Quantum Mechanics 187 // 3.3 The State of a System 190 // 3.3.1 Probability Density 190 // 3.3.2 The Superposition Principle 191 // 3.4 Observables and Operators 193 // 3.5 Measurement in Quantum Mechanics 195 // 3.5.1 How Measurements Disturb Systems 195 // 3.5.2 Expectation Values 196 // 3.5.3 Complete Sets of Commuting Operators (CSCO) 198 // 3.5.4 Measurement and the Uncertainty Relations 200 // 3.6 Time Evolution of the System’s State 201 // 3.6.1 Time Evolution Operator 201 // 3.6.2 Stationary States: Time-Independent Potentials 202 // 3.6.3 Schrödinger Equation and Wave Packets 203 // 3.6.4 The Conservation of Probability 204 // 3.6.5 Time Evolution of Expectation Values 206 // 3.7 Symmetries and Conservation Laws 207 // 3.7.1 Infinitesimal Unitary Transformations 207 // 3.7.2 Finite Unitary Transformations 208 // 3.7.3 Symmetries and Conservation Laws 209 //

3.8 Connecting Quantum to Classical Mechanics 211 // 3.8.1 Poisson Brackets and Commutators 211 // 3.8.2 The Ehrenfest Theorem 213 // 3.8.3 Quantum Mechanics and Classical Mechanics 214 // 3.9 Solved Problems 216 // 3.10 Exercises 234 // 4 One-Dimensional Problems 241 // 4.1 Introduction 241 // 4.2 Properties of One-Dimensional Motion 242 // 4.2.1 Discrete Spectrum (Bound States) 242 // 4.2.2 Continuous Spectrum (Unbound States) 243 // 4.2.3 Mixed Spectrum 243 // 4.2.4 Symmetric Potentials and Parity 244 // 4.3 The Free Particle: Continuous States 244 // 4.4 The Potential Step 246 // 4.5 The Potential Barrier and Well 250 // 4.5.1 The Case E > Vq 250 // 4.5.2 The Case E < Vq: Tunneling 254 // 4.5.3 The Tunneling Effect 257 // 4.6 The Infinite Square Well Potential 258 // 4.6.1 The Asymmetric Square Well 258 // 4.6.2 The Symmetric Potential Well 261 // 4.7 The Finite Square Well Potential 262 // 4.7.1 The Scattering Solutions (E > Vo) 262 // 4.7.2 The Bound State Solutions (0 < E < Vo) 262 // 4.8 The Harmonic Oscillator 266 // 4.8.1 Energy Eigenvalues 269 // 4.8.2 Energy Eigenstates 271 // 4.8.3 Energy Eigenstates in Position Space 272 // 4.8.4 The Matrix Representation of Various Operators 275 // 4.8.5 Expectation Values of Various Operators 276 // 4.9 Numerical Solution of the Schrödinger Equation 277 // 4.9.1 Numerical Procedure 277 // 4.9.2 Algorithm 279 // 4.10 Solved Problems 281 // 4.11 Exercises 305 // 5 Angular Momentum 313 // 5.1 Introduction 313 // 5.2 Orbital Angular Momentum 313 // 5.3 General Formalism of Angular Momentum 315 // 5.4 Matrix Representation of Angular Momentum 320 // 5.5 Geometrical Representation of Angular Momentum 323 // 5.6 Spin Angular Momentum 325 // 5.6.1 Experimental Evidence of the Spin 325 // 5.6.2 General Theory of Spin 329 // 5.6.3 Spin 1/2 and the Pauli Matrices 330 // 5.6.4 Schrodinger Equation with Spin: Pauli Hamiltonian 333 //

5.7 Eigenfunctions of the Orbital Angular Momentum 335 // 5.7.1 Eigenfunctions and Eigenvalues of Lz 336 // 5.7.2 Eigenfunctions of L2 336 // 5.7.3 Properties of the Spherical Harmonics 340 // 5.8 Solved Problems 344 // 5.9 Exercises 359 // 6 Three-Dimensional Problems 367 // 6.1 Introduction 367 // 6.2 3D Problems in Cartesian Coordinates 367 // 6.2.1 General Treatment: Separation of Variables 367 // 6.2.2 The Free Particle 369 // 6.2.3 The Box Potential 370 // 6.2.4 The Harmonic Oscillator 372 // 6.3 3D Problems in Spherical Coordinates 374 // 6.3.1 Central Potential: General Treatment 374 // 6.3.2 The Free Particle in Spherical Coordinates 378 // 6.3.3 The Spherical Square Well Potential 380 // 6.3.4 The Isotropic Harmonic Oscillator 382 // 6.3.5 The Hydrogen Atom 385 // 6.3.6 Effect of Magnetic Fields on Central Potentials 400 // 6.4 Pauli Equation for a Spin 1/2 Particle in a Magnetic Field 403 // 6.4.1 Pauli equation for a free Spin 1/2 Particle 404 // 6.4.2 Pauli equation for a Spin 1/2 Particle in an Electromagnetic Field 405 // 6.5 Concluding Remarks 408 // 6.6 Solved Problems 410 // 6.7 Exercises 427 // 7 Rotations and Addition of Angular Momenta 433 // 7.1 Rotations in Classical Physics 433 // 7.1.1 Active Rotations 433 // 7.1.2 Passive Rotations 434 // 7.1.3 Properties of Rotation Matrices 436 // 7.2 Rotations in Quantum Mechanics 437 // 7.2.1 Infinitesimal Rotations 438 // 7.2.2 Finite Rotations 439 // 7.2.3 Properties of the Rotation Operator 440 // 7.2.4 Euler Rotations 442 // 7.2.5 Representation of the Rotation Operator 443 // 7.2.6 Rotation Matrices and the Spherical Harmonics 445 // 7.3 Addition of Angular Momenta 448 // 7.3.1 Addition of Two Angular Momenta: General Formalism 448 // 7.3.2 Calculation of the Clebsch-Gordan Coefficients 454 // 7.3.3 Coupling of Orbital and Spin Angular Momenta 460 // 7.3.4 Addition of More Than Two Angular Momenta 464 //

7.3.5 Rotation Matrices for Coupling Two Angular Momenta 465 // 7.3.6 Isospin 468 // 7.4 Rotations of Scalar, Vector, and Tensor Operators 471 // 7.4.1 Transformation of Scalar Operators Under Rotations 471 // 7.4.2 Transformation of Vector Operators Under Rotations 472 // 7.4.3 Transformation of Tensor Operators Under Rotations 473 // 7.4.4 Wigner-Eckart Theorem for Spherical Tensor Operators 476 // 7.5 Solved Problems 479 // 7.6 Exercises 496 // 8 Identical Particles 503 // 8.1 Many-Particle Systems 503 // 8.1.1 Schrodinger Equation 503 // 8.1.2 Interchange Symmetry 505 // 8.1.3 Systems of Distinguishable Noninteracting Particles 506 // 8.2 Systems of Identical Particles 508 // 8.2.1 Identical Particles in Classical and Quantum Mechanics 508 // 8.2.2 Exchange Degeneracy 510 // 8.2.3 Symmetrization Postulate 511 // 8.2.4 Constructing Symmetric and Antisymmetric Functions 512 // 8.2.5 Systems of Identical Noninteracting Particles 513 // 8.3 The Pauli Exclusion Principle 516 // 8.4 The Exclusion Principle and the Periodic Table 517 // 8.5 Solved Problems 524 // 8.6 Exercises 533 // 9 Approximation Methods for Stationary States 537 // 9.1 Introduction 537 // 9.2 Time-Independent Perturbation Theory 538 // 9.2.1 Nondegenerate Perturbation Theory 538 // 9.2.2 Degenerate Perturbation Theory 544 // 9.2.3 Fine Structure and the Anomalous Zeeman Effect 548 // 9.3 The Variational Method 558 // 9.4 The Wentzel-Kramers-Brillouin Method 566 // 9.4.1 General Formalism 566 // 9.4.2 Bound States for Potential Wells with No Rigid Walls 569 // 9.4.3 Bound States for Potential Wells with One Rigid Wall 575 // 9.4.4 Bound States for Potential Wells with Two Rigid Walls 577 // 9.4.5 Tunneling through a Potential Barrier 579 // 9.5 Concluding Remarks 582 // 9.6 Solved Problems 582 // 9.7 Exercises 614 // 10 Time-Dependent Perturbation Theory 623 // 10.1 Introduction 623 //

10.2 The Pictures of Quantum Mechanics 623 // 10.2.1 The Schrodinger Picture 624 // 10.2.2 The Heisenberg Picture 624 // 10.2.3 The Interaction Picture 625 // 10.3 Time-Dependent Perturbation Theory 627 // 10.3.1 Transition Probability 629 // 10.3.2 Transition Probability for a Constant Perturbation 630 // 10.3.3 Transition Probability for a Harmonic Perturbation 631 // 10.4 Adiabatic and Sudden Approximations 635 // 10.4.1 Adiabatic Approximation 635 // 10.4.2 Sudden Approximation 636 // 10.5 Interaction of Atoms with Radiation 639 // 10.5.1 Classical Treatment of the Incident Radiation 640 // 10.5.2 Quantization of the Electromagnetic Field 641 // 10.5.3 Transition Rates for Absorption and Emission of Radiation 644 // 10.5.4 Transition Rates within the Dipole Approximation 645 // 10.5.5 The Electric Dipole Selection Rules 646 // 10.5.6 Spontaneous Emission 647 // 10.6 Solved Problems 650 // 10.7 Exercises 667 // 11 Scattering Theory 671 // 11.1 Scattering and Cross Section 671 // 11.1.1 Connecting the Angles in the Lab and CM frames 672 // 11.1.2 Connecting the Lab and CM Cross Sections 674 // 11.2 Scattering Amplitude of Spinless Particles 675 // 11.2.1 Scattering Amplitude and Differential Cross Section 678 // 11.2.2 Scattering Amplitude 678 // 11.3 The Bom Approximation 682 // 11.3.1 The First Bom Approximation 682 // 11.3.2 Validity of the First Bom Approximation 683 // 11.4 Partial Wave Analysis 685 // 11.4.1 Partial Wave Analysis for Elastic Scattering 685 // 11.4.2 Partial Wave Analysis for Inelastic Scattering 689 // 11.5 Scattering of Identical Particles 691 // 11.6 Solved Problems 693 // 11.7 Exercises 704 // 12 Relativistic Quantum Mechanics 707 // 12.1 Introduction 707 // 12.2 Four Vectors and Minkowski Metric 709 // 12.2.1 Euclidean Metric 709 // 12.2.2 Minkowski Spacetime and the Lorentz Transformation 710 // 12.2.3 Four-Vectors 711 //

12.2.4 Minkowski Metric 712 // 12.3 Klein-Gordon Equation 715 // 12.3.1 Historical note about the Genesis of the Klein-Gordon Equation 715 // 12.3.2 Klein-Gordon Equation for a Free particle and its Covariance 717 // 12.3.3 Nonrelativistic Limit of the Klein-Gordon Equation 719 // 12.3.4 Conceptual Problems of the Klein-Gordon Equation 721 // 12.3.5 Klein Paradox for Spin-Zero Particles 725 // 12.3.6 Klein-Gordon Equation in an Electromagnetic Field 731 // 12.3.7 Non-Relativistic Limit of the KGE in an Electromagnetic Field 732 // 12.4 Dirac Equation 734 // 12.4.1 Dirac Equation for a Free Particle 735 // 12.4.2 Representation of the Dirac Matrices 737 // 12.4.3 Dirac Matrices and their Properties 739 // 12.4.4 Dirac, Weyl, and Majorana Representations of the y Matrices 746 // 12.4.5 Dirac Equation in Covariant Form 748 // 12.4.6 Lorentz Covariance of the Dirac Equation 749 // 12.4.7 Continuity Equation and Current Conservation 753 // 12.4.8 Solutions of the Dirac Equation for a Free Particle at Rest 756 // 12.4.9 Solutions of the Dirac Equation for a Free Particle in Motion 760 // 12.4.10 Negative-Energies Interpretation: Dirac’s Hole Theory 763 // 12.4.11 Negative-Energies Interpretation: Feynman-Stuckelberg Method 766 // 12.4.12 Negative-Energies Interpretation: Klein Paradox for Spin-1/2 Particles 773 // 12.4.13 Spin-Half Solutions of the Dirac Equation 777 // 12.4.14 Helicity 782 // 12.4.15 Dirac Equation for Massless Particles: Weyl Fermions 784 // 12.4.16 Weyl Spinors and Parity Violation 786 // 12.4.17 Weyl Fermions and Neutrinos 786 // 12.4.18 Chirality 789 // 12.4.19 Dirac Equation in an Electromagnetic Field 793 // 12.4.20 Non-relativistic limit of the Dirac Equation 794 // 12.4.21 Discrete Symmetries of the Dirac Equation 800 // 12.4.22 Charge Conjugation and Covariance of the Dirac Equation 800 // 12.4.23 Parity and Covariance of the Dirac Equation 805 //

12.4.24 Time-Reversal and Covariance of the Dirac Equation 810 // 12.4.25 The CPT Theorem 815 // 12.5 Successes and Limitations of Relativistic Quantum Mechanics 817 // 12.6 Beyond Relativistic Quantum Mechanics 819 // 12.7 Solved Problems 819 // 12.8 Exercises 889 // 13 Beyond Relativistic Quantum Mechanics 897 // 13.1 Introduction 897 // 13.2 Advantages of Lagrangians in Field Theories 898 // 13.3 Lagrangians in Classical Field Theory 899 // 13.4 Lagrangian Derivation of the Maxwell Equations 903 // 13.4.1 Maxwell Equations in Differential Form 903 // 13.4.2 Maxwell Equations in Covariant Form 905 // 13.4.3 Lagrangian Derivation of the Maxwell Equations 909 // 13.5 Lagrangian Derivation of the Klein-Gordon Equation 911 // 13.6 Lagrangian Derivation of the Dirac Equation 915 // 13.7 Beyond Classical Field Theory: Quantum Field Theory 919 // 13.8 The Lagrangian of Quantum Electrodynamics 920 // 13.9 Concluding Thoughts 922 // 13.10Sol ved Problems 923 // 13.11 Exercises 934 // A The Delta Function 937 // A.1 One-Dimensional Delta Function 937 // A.1.1 Various Definitions of the Delta Function 937 // A.1.2 Properties of the Delta Function 938 // A.1.3 Derivative of the Delta Function 939 // A.2 Three-Dimensional Delta Function 940 // B Angular Momentum in Spherical Coordinates 941 // B.l Derivation of Some General Relations 941 // B.2 Gradient and Laplacian in Spherical Coordinates 942 // B.3 Angular Momentum in Spherical Coordinates 943 // C C++ Code for Solving the Schrödinger Equation 945 // C.l Introduction 945 // C.2 C++ Code for Solving the Schrödinger Equation 945 // D Index Notation for 4-Vectors 951 // D.l Index Notation for 3 and 4-Vectors 951 // D.l.l Introductory Reminder 951 // D.l.2 Index Notation for 3-Vectors 953 // D.1.3 Inner and Cross Products of 3-Vectors in the Index Notation 954 // D.1.4 Index Notation for 4-Vectors 956 //

D.2 The Minkowski Metric 957 // E The Relativistic Notation and Four Vectors 961 // E.l Introduction 961 // E.2 Lorentz transformation 962 // E.3 Minkowski Spacetime 964 // E.4 The 4-Vector Notation 964 // E.5 Contravariant and Covariant notations 968 // E.6 Lorentz transformation in the contravariant-covariant form 974 // E.7 Invariance under the Lorentz transformation 977 // F Lagrangian Formulation of Classical Mechanics 979 // F.l Lagrangian Formulation of Classical Mechanics 979 // F.2 Hamiltonian Formulation of Classical Mechanics 984 // F.3 Canonical Quantization: from Classical to Quantum Mechanics 989 // Index 993