Quantum mechanics : concepts and applications / Nouredine Zettili.

Format:

Book

Author/Creator:

Zettili, Nouredine.

Language:

English

Subjects (All):

Quantum theory.

Physical Description:

xiv, 649 pages : illustrations ; 25 cm

Place of Publication:

Chichester ; New York : Wiley, [2001]

Summary:

This richly illustrated textbook provides a clear, balanced and modern approach to quantum mechanics. It combines the essential elements of the theory with the practical applications. Containing many examples and problems with step-by-step solutions, this cleverly structured text assists the reader in mastering the machinery of quantum mechanics. A comprehensive introduction to the subject Includes over 65 solved examples integrated throughout the text Includes over 154 fully solved multipart problems Offers an indepth treatment of the practical mathematical tools of quantum mechanics Accessible to teachers as well as students

Contents:

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 15

1.3 Wave Aspect of Particles 17

1.3.1 de Broglie's Hypothesis: Matter Waves 17

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 21

1.4.1 Classical View of Particles and Waves 21

1.4.2 Quantum View of Particles and Waves 23

1.4.3 Wave-Particle Duality: Complementarity 25

1.4.4 Principle of Linear Superposition 26

1.5 Indeterministic Nature of the Microphysical World 27

1.5.1 Heisenberg Uncertainty Principle 27

1.5.2 Probabilistic Interpretation 29

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 30

1.7 Quantization Rules 36

1.8 Wave Packets 38

1.8.1 Localized Wave Packets 38

1.8.2 Wave Packets and the Uncertainty Relations 41

1.8.3 Motion of Wave Packets 42

2 Mathematical Tools of Quantum Mechanics 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-Integrable Functions: Wave Functions 83

2.3 Dirac Notation 84

2.4 Operators 88

2.4.2 Hermitian Adjoint 89

2.4.3 Projection Operators 91

2.4.4 Commutator Algebra 92

2.4.5 Uncertainty Relation between Two Operators 94

2.4.6 Functions of Operators 95

2.4.7 Inverse and Unitary Operators 96

2.4.8 Eigenvalues and Eigenvectors of an Operator 97

2.4.9 Infinitesimal and Finite Unitary Transformations 100

2.5 Representation in Discrete Bases 102

2.5.1 Matrix Representation of Kets, Bras and Operators 103

2.5.2 Change of Bases and Unitary Transformations 111

2.5.3 Matrix Representation of the Eigenvalue Problem 114

2.6 Representation in Continuous Bases 117

2.6.1 General Treatment 117

2.6.2 Position Representation 119

2.6.3 Momentum Representation 120

2.6.4 Connecting the Position and Momentum Representations 120

2.6.5 Parity Operator 124

2.7 Matrix and Wave Mechanics 126

2.7.1 Matrix Mechanics 126

2.7.2 Wave Mechanics 127

3 Postulates of Quantum Mechanics 157

3.2 The Basic Postulates of Quantum Mechanics 157

3.3 The State of a System 159

3.3.1 Probability Density 159

3.3.2 The Superposition Principle 160

3.4 Observables and Operators 162

3.5 Measurement in Quantum Mechanics 164

3.5.1 How Measurements Disturb Systems 164

3.5.2 Expectation Values 165

3.5.3 Complete Sets of Commuting Operators 167

3.5.4 Measurement and the Uncertainty Relations 169

3.6 Time Evolution of the System's State 170

3.6.1 Time Evolution Operator 170

3.6.2 Stationary States: Time-Independent Potentials 171

3.6.3 Schrodinger Equation and Wave Packets 172

3.6.4 The Conservation of Probability 173

3.6.5 Time Evolution of Expectation Values 174

3.7 Symmetries and Conservation Laws 175

3.7.1 Infinitesimal Unitary Transformations 175

3.7.2 Finite Unitary Transformations 176

3.7.3 Symmetries and Conservation Laws 177

3.8 Connecting Quantum to Classical Mechanics 179

3.8.1 Poisson Brackets and Commutators 179

3.8.2 The Ehrenfest Theorem 181

3.8.3 Quantum Mechanics and Classical Mechanics 182

4 One-Dimensional Problems 205

4.2 Properties of One-Dimensional Motion 206

4.2.1 Discrete Spectrum (Bound States) 206

4.2.2 Continuous Spectrum (Unbound States) 207

4.2.3 Mixed Spectrum 207

4.2.4 Symmetric Potentials and Parity 207

4.3 The Free Particle: Continuous States 208

4.4 The Potential Step 210

4.5 The Potential Barrier and Well 213

4.5.1 The Case E > V[subscript 0] 214

4.5.2 The Case E < V[subscript 0]: Tunneling 216

4.5.3 The Tunneling Effect 219

4.6 The Infinite Square Well Potential 220

4.6.1 The Unsymmetric Square Well 220

4.6.2 The Symmetric Potential Well 223

4.7 The Finite Square Well Potential 224

4.7.1 The Scattering Solutions (E > V[subscript 0]) 224

4.7.2 The Bound State Solutions (0 < E < V[subscript 0]) 224

4.8 The Harmonic Oscillator 227

4.8.1 Energy Eigenvalues 229

4.8.2 Energy Eigenstates 231

4.8.3 Energy Eigenstates in Position Space 231

4.8.4 The Matrix Representation of Various Operators 234

4.8.5 Expectation Values of Various Operators 235

4.9 Numerical Solution of the Schrodinger Equation 236

4.9.1 Numerical Procedure 236

4.9.2 Algorithm 237

5 Angular Momentum 269

5.2 Orbital Angular Momentum 269

5.3 General Formalism of Angular Momentum 271

5.4 Matrix Representation of Angular Momentum 276

5.5 Geometrical Representation of Angular Momentum 279

5.6 Spin Angular Momentum 280

5.6.1 Experimental Evidence of the Spin 280

5.6.2 General Theory of Spin 283

5.6.3 Spin 1/2 and the Pauli Matrices 284

5.7 Eigenfunctions of Orbital Angular Momentum 287

5.7.1 Eigenfunctions and Eigenvalues of L[subscript z] 288

5.7.2 Eigenfunctions of L[superscript 2] 289

5.7.3 Properties of the Spherical Harmonics 292

6 Three-Dimensional Problems 317

6.2 3D Problems in Cartesian Coordinates 317

6.2.1 General Treatment: Separation of Variables 317

6.2.2 The Free Particle 319

6.2.3 The Box Potential 320

6.2.4 The Harmonic Oscillator 322

6.3 3D Problems in Spherical Coordinates 324

6.3.1 Central Potential: General Treatment 324

6.3.2 The Free Particle in Spherical Coordinates 327

6.3.3 The Spherical Square Well Potential 329

6.3.4 The Isotropic Harmonic Oscillator 330

6.3.5 The Hydrogen Atom 334

6.3.6 Effect of Magnetic Fields on Central Potentials 348

7 Rotations and Addition of Angular Momenta 373

7.1 Rotations in Classical Physics 373

7.2 Rotations in Quantum Mechanics 375

7.2.1 Infinitesimal Rotations 375

7.2.2 Finite Rotations 377

7.2.3 Properties of the Rotation Operator 378

7.2.4 Euler Rotations 379

7.2.5 Representation of the Rotation Operator 380

7.2.6 Rotation Matrices and the Spherical Harmonics 382

7.3 Addition of Angular Momenta 385

7.3.1 Addition of Two Angular Momenta: General Formalism 385

7.3.2 Calculation of the Clebsch-Gordan Coefficients 391

7.3.3 Coupling of Orbital and Spin Angular Momenta 397

7.3.4 Addition of More Than Two Angular Momenta 401

7.3.5 Rotation Matrices for Coupling Two Angular Momenta 402

7.3.6 Isospin 404

7.4 Scalar, Vector and Tensor Operators 407

7.4.1 Scalar Operators 408

7.4.2 Vector Operators 408

7.4.3 Tensor Operators: Reducible and Irreducible Tensors 410

7.4.4 Wigner-Eckart Theorem for Spherical Tensor Operators 412

8 Identical Particles 437

8.1 Many-Particle Systems 437

8.1.1 Schrodinger Equation 437

8.1.2 Interchange Symmetry 439

8.1.3 Systems of Distinguishable Noninteracting Particles 440

8.2 Systems of Identical Particles 442

8.2.1 Identical Particles in Classical and Quantum Mechanics 442

8.2.2 Exchange Degeneracy 444

8.2.3 Symmetrization Postulate 445

8.2.4 Constructing Symmetric and Antisymmetric Functions 446

8.2.5 Systems of Identical Noninteracting Particles 446

8.3 The Pauli Exclusion Principle 449

8.4 The Exclusion Principle and the Periodic Table 451

9 Approximation Methods for Stationary States 469

9.2 Time-Independent Perturbation Theory 470

9.2.1 Nondegenerate Perturbation Theory 470

9.2.2 Degenerate Perturbation Theory 476

9.2.3 Fine Structure and the Anomalous Zeeman Effect 479

9.3 The Variational Method 488

9.4 The Wentzel-Kramers-Brillouin Method 495

9.4.1 General Formalism 495

9.4.2 Bound States for Potential Wells with No Rigid Walls 498

9.4.3 Bound States for Potential Wells with One Rigid Wall 504

9.4.4 Bound States for Potential Wells with Two Rigid Walls 505

9.4.5 Tunneling through a Potential Barrier 507

10 Time-Dependent Perturbation Theory 549

10.2 The Pictures of Quantum Mechanics 549

10.2.1 The Schrodinger Picture 550

10.2.2 The Heisenberg Picture 550

10.2.3 The Interaction Picture 551

10.3 Time-Dependent Perturbation Theory 552

10.3.1 Transition Probability 554

10.3.2 Transition Probability for a Constant Perturbation 555

10.3.3 Transition Probability for a Harmonic Perturbation 557

10.4 Adiabatic and Sudden Approximations 560

10.4.1 Adiabatic Approximation 560

10.4.2 Sudden Approximation 561

10.5 Interaction of Atoms with Radiation 564

10.5.1 Classical Treatment of the Incident Radiation 565

10.5.2 Quantization of the Electromagnetic Field 566

10.5.3 Transition Rates for Absorption and Emission of Radiation 569

10.5.4 Transition Rates within the Dipole Approximation 570

10.5.5 The Electric Dipole Selection Rules 571

10.5.6 Spontaneous Emission 572

11 Scattering Theory 595

11.1 Scattering and Cross Section 595

11.1.1 Connecting the Angles in the Lab and CM frames 596

11.1.2 Connecting the Lab and CM Cross Sections 598

11.2 Scattering Amplitude of Spinless Particles 599

11.2.1 Scattering Amplitude and Differential Cross Section 601

11.2.2 Scattering Amplitude 602

11.3 The Born Approximation 606

11.3.1 The First Born Approximation 606

11.3.2 Validity of the First Born Approximation 607

11.4 Partial Wave Analysis 609

11.4.1 Partial Wave Analysis for Elastic Scattering 609

11.4.2 Partial Wave Analysis for Inelastic Scattering 613

11.5 Scattering of Identical Particles 614

A The Delta Function 629

A.1 One-Dimensional Delta Function 629

A.1.1 Various Definitions of the Delta Function 629

A.1.2 Properties of the Delta Function 630

A.1.3 Derivative of the Delta Function 631

A.2 Three-Dimensional Delta Function 631

B Angular Momentum in Spherical Coordinates 633

B.1 Derivation of Some General Relations 633

B.2 Gradient and Laplacian in Spherical Coordinates 634

B.3 Angular Momentum in Spherical Coordinates 635

C Computer Code for Solving the Schrodinger Equation 637.

Notes:

Includes bibliographical references (pages 641-642) and index.

ISBN:

0471489433

0471489441

OCLC:

46857540

Online:

Table of Contents