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EB

EB

ONLINE

3rd ed.

Cambridge : Cambridge University Press, 2018

1 online zdroj (516 stran)

ISBN 9781108103145 (e-kniha)

ISBN 9781107189638 (print)

Print version: Griffiths, David J. Introduction to Quantum Mechanics Cambridge : Cambridge University Press,c2018 ISBN 9781107189638

This widely-used and time-tested textbook is indispensable for teachers and students of quantum mechanics, one of the essential foundations of modern physics. It is also useful as a reference for those in related fields (engineering, mathematics, chemistry), or for self-study by non-professionals..

002001783

Preface page xi // I THEORY 1 // 1 The Wave Function 3 // 1.1 The Schrödinger Equation 3 // 1.2 The Statistical Interpretation 3 // 1.3 Probability 8 // 1.3.1 Discrete Variables 8 // 1.3.2 Continuous Variables H // 1.4 Normalization 14 // 1.5 Momentum 16 // 1.6 The Uncertainty Principle 19 // Further Problems on Chapter 1 20 // 2 Time-Independent Schrödinger Equation 25 // 2.1 Stationary States 25 // 2.2 The Infinite Square Well 31 // 2.3 The Harmonic Oscillator 39 // 2.3.1 Algebraic Method 40 // 2.3.2 Analytic Method 48 // 2.4 The Free Particle 35 // 2.5 The Delta-Function Potential 61 // 2.5.1 Bound States and Scattering States 61 // 2.5.2 The Delta-Function Well 63 // 2.6 The Finite Square Well 20 // Further Problems on Chapter 2 76 // 3 Formalism 91 // 3.1 Hilbert Space 91 // 3.2 Observables 94 // 3.2.1 Hcrmitian Operators 94 // 3.2.2 Determinate States 96 // Contents // 3.3 Eigenfunctions of a Hcrmitian Operator 97 // 3.3.1 Discrete Spectra 98 // 3.3.2 Continuous Spectra 99 // 3.4 Generalized Statistical Interpretation 102 // 3.5 The Uncertainty Principle 105 // 3.5.1 Proof of the Generalized Uncertainty Principle 105 // 3.5.2 The Minimum-Uncertainty Wave Packet 108 // 3.5.3 The Energy-Time Uncertainty Principle 109 // 3.6 Vectors and Operators 113 // 3.6.1 Bases in Hilbert Space 113 // 3.6.2 Dirac Notation 117 // 3.6.3 Changing Bases in Dirac Notation 121 // Further Problems on Chapter 3 124 // 4 Quantum Mechanics in Three Dimensions 131 // 4.1 The Schrödinger Equation 131 // 4.1.1 Spherical Coordinates 132 // 4.1.2 The Angular Equation 134 // 4.1.3 The Radial Equation 138 // 4.2 The Hydrogen Atom 143 // 4.2.1 The Radial Wave Function 144 // 4.2.2 The Spectrum of Hydrogen 155 // 4.3 Angular Momentum 157 // 4.3.1 Eigenvalues 157 // 4.3.2 Eigenfunctions 162 // 4.4 Spin 165 // 4.4.1 Spin 1/2 167 // 4.4.2 Electron in a Magnetic Field 172 //

4.4.3 Addition of Angular Momenta 176 // 4.5 Electromagnetic Interactions 181 // 4.5.1 Minimal Coupling 181 // 4.5.2 The Aharonov-Bohm Effect 182 // Further Problems on Chapter 4 187 // 5 Identical Particles 198 // 5.1 Two-Particle Systems 198 // 5.1.1 Bosons and Fermions 201 // 5.1.2 Exchange Forces 203 // Contents // vii // 5.1.3 Spin 206 // 5.1.4 Generalized Symmetrization Principle 207 // 5.2 Atoms 209 // 5.2.1 Helium 210 // 5.2.2 The Periodic Table 213 // 5.3 Solids 216 // 5.3.1 The Free Electron Gas 216 // 5.3.2 Band Structure 220 // Further Problems on Chapter 5 225 // 6 Symmetries & Conservation Laws 232 // 6.1 Introduction 232 // 6.1.1 Transformations in Space 232 // 6.2 The Translation Operator 235 // 6.2.1 How Operators Transform 235 // 6.2.2 Translational Symmetry 238 // 6.3 Conservation Laws 242 // 6.4 Parity 243 // 6.4.1 Parity in One Dimension 243 // 6.4.2 Parity in Three Dimensions 244 // 6.4.3 Parity Selection Rules 246 // 6.5 Rotational Symmetry 248 // 6.5.1 Rotations About the z Axis 248 // 6.5.2 Rotations in Three Dimensions 249 // 6.6 Degeneracy 252 // 6.7 Rotational Selection Rules 255 // 6.7.1 Selection Rules for Scalar Operators 255 // 6.7.2 Selection Rules for Vector Operators 258 // 6.8 Translations in Time 262 // 6.8.1 The Heisenberg Picture 264 // 6.8.2 Time-Translation Invariance 266 // Further Problems on Chapter 6 268 // II APPLICATIONS 277 // 7 Time-Independent Perturbation Theory 279 // 7.1 Nondegenerate Perturbation Theory 279 // 7.1.1 General Formulation 279 // 7.1.2 First-Order Theory 280 // 7.1.3 Second-Order Energies 284 // 7.2 Degenerate Perturbation Theory 286 // 7.2.1 Two-Fold Degeneracy 286 // 7.2.2 “Good” States 291 // 7.2.3 Higher-Order Degeneracy 294 // 7.3 The Fine Structure of Hydrogen 295 // 7.3.1 The Relativistic Correction 296 // 73.2 Spin-Orbit Coupling 299 // 7.4 The Zeeman Effect 304 //

7.4.1 Weak-Field Zeeman Effect 305 // 7.4.2 Strong-Field Zeeman Effect 307 // 7.4.3 Intermediate-Field Zeeman Effect 309 // 7.5 Hyperfine Splitting in Hydrogen 311 // Further Problems on Chapter 7 313 // 8 The Variational Principle 327 // 8.1 Theory 327 // 8.2 The Ground State of Helium 332 // 8.3 The Hydrogen Molecule Ion 337 // 8.4 The Hydrogen Molecule 341 // Further Problems on Chapter 8 346 // 9 The WKB Approximation 354 // 9.1 The “Classical” Region 354 // 9.2 Tunneling 358 // 9.3 The Connection Formulas 362 // Further Problems on Chapter 9 371 // 10 Scattering 376 // 10.1 Introduction 376 // 10.1.1 Classical Scattering Theory 376 // 10.1.2 Quantum Scattering Theory 379 // 10.2 Partial Wave Analysis 380 // 10.2.1 Formalism 380 // 10.2.2 Strategy 383 // 10.3 Phase Shifts 385 // 10.4 The Born Approximation 388 // 10.4.1 Integral Form or the Schrödinger Equation 388 // 10.4.2 The First Born Approximation 391 // 10.4.3 The Born Series 395 // Further Problems on Chapter 10 397 // 11 Quantum Dynamics 402 // 11.1 Two-Level Systems 403 // 11.1.1 The Perturbed System 403 // 11.1.2 Time-Dependent Perturbation Theory 405 // 11.1.3 Sinusoidal Perturbations 408 // 11.2 Emission and Absorption of Radiation 411 // 11.2.1 Electromagnetic Waves 411 // 11.2.2 Absorption, Stimulated Emission, and Spontaneous Emission 412 // 11.2.3 Incoherent Perturbations 413 // 11.3 Spontaneous Emission 416 // 11.3.1 Einstein’s A and ? Coefficients 416 // 11.3.2 The Lifetime of an Excited State 418 // 11.3.3 Selection Rules 420 // 11.4 Fermi’s Golden Rule 422 // 11.5 The Adiabatic Approximation 426 // 11.5.1 Adiabatic Processes 426 // 11.5.2 The Adiabatic Theorem 428 // Further Problems on Chapter 11 433 // 12 Afterword 446 // 12.1 The RPR Paradox 447 // 12.2 Bell’s Theorem 449 // 12.3 Mixed States and the Density’ Matrix 455 // 12.3.1 Pure States 455 // 12.3.2 Mixed States 456 //

12.3.3 Subsystems 458 // 12.4 The No-Clone Theorem 459 // 12.5 Schrödinger’s Cat 461 // Appendix Linear Algebra 464 // A.l Vectors 464 // A.2 Inner Products 466 // A.3 Matrices // ?.4 Changing Bases // A.5 Eigenvectors and Eigenvalues // A.6 Hermitian Transformations // Index 486

(MiAaPQ)EBC31853976

(Au-PeEL)EBL31853976

(OCoLC)1493001313