Applied quantum mechanics / A.F.J. Levi.

Format:

Book

Author/Creator:

Levi, A. F. J. (Anthony Frederic John), 1959-

Language:

English

Subjects (All):

Quantum theory.

Physical Description:

xvi, 558 pages : illustrations ; 26 cm

Edition:

Second edition.

Place of Publication:

Cambridge ; New York : Cambridge University Press, 2006.

Summary:

Electrical and mechanical engineers, materials scientist, and applied physicists will find Levi's uniquely practical explanation of quantum mechanics invaluable. This updated and expanded edition of the bestselling original text now covers quantization of angular momentum and quantum communication, and problems and additional references are included. Using real-world engineering examples to engage the reader, the author makes quantum mechanics accessible and relevant to the engineering student. Numerous illustrations, exercises, worked examples, and problems are included.

Contents:

MATLAB programs xvi

1.1 Motivation 1

1.2 Classical mechanics 4

1.2.2 The one-dimensional simple harmonic oscillator 7

1.2.3 Harmonic oscillation of a diatomic molecule 10

1.2.4 The monatomic linear chain 13

1.2.5 The diatomic linear chain 15

1.3 Classical electromagnetism 18

1.3.1 Electrostatics 18

1.3.2 Electrodynamics 24

2 Toward quantum mechanics 57

2.1.1 Diffraction and interference of light 58

2.1.2 Black-body radiation and evidence for quantization of light 62

2.1.3 Photoelectric effect and the photon particle 64

2.1.4 Secure quantum communication 66

2.1.5 The link between quantization of photons and other particles 70

2.1.6 Diffraction and interference of electrons 71

2.1.7 When is a particle a wave? 72

2.2 The Schrodinger wave equation 73

2.2.1 The wave function description of an electron in free space 79

2.2.2 The electron wave packet and dispersion 80

2.2.3 The hydrogen atom 83

2.2.4 Periodic table of elements 89

2.2.5 Crystal structure 93

2.2.6 Electronic properties of bulk semiconductors and heterostructures 96

3 Using the Schrodinger wave equation 117

3.1.1 The effect of discontinuity in the wave function and its slope 118

3.2 Wave function normalization and completeness 121

3.3 Inversion symmetry in the potential 122

3.3.1 One-dimensional rectangular potential well with infinite barrier energy 123

3.4 Numerical solution of the Schrodinger equation 126

3.5 Current flow 128

3.5.1 Current in a rectangular potential well with infinite barrier energy 129

3.5.2 Current flow due to a traveling wave 131

3.6 Degeneracy as a consequence of symmetry 131

3.6.1 Bound states in three dimensions and degeneracy of eigenvalues 131

3.7 Symmetric finite-barrier potential 133

3.7.1 Calculation of bound states in a symmetric finite-barrier potential 135

3.8 Transmission and reflection of unbound states 137

3.8.1 Scattering from a potential step when m[subscript 1] = m[subscript 2] 138

3.8.2 Scattering from a potential step when m[subscript 1] [not equal] m[subscript 2] 140

3.8.3 Probability current density for scattering at a step 141

3.8.4 Impedance matching for unity transmission across a potential step 142

3.9 Particle tunneling 145

3.9.1 Electron tunneling limit to reduction in size of CMOS transistors 149

3.10 The nonequilibrium electron transistor 150

4 Electron propagation 171

4.2 The propagation matrix method 172

4.3 Program to calculate transmission probability 177

4.4 Time-reversal symmetry 178

4.5 Current conservation and the propagation matrix 180

4.6 The rectangular potential barrier 182

4.6.1 Transmission probability for a rectangular potential barrier 182

4.6.2 Transmission as a function of energy 185

4.6.3 Transmission resonances 186

4.7 Resonant tunneling 188

4.7.1 Heterostructure bipolar transistor with resonant tunnel-barrier 190

4.7.2 Resonant tunneling between two quantum wells 192

4.8 The potential barrier in the delta function limit 197

4.9 Energy bands in a periodic potential 199

4.9.1 Bloch's Theorem 200

4.9.2 The propagation matrix applied to a periodic potential 201

4.9.3 The tight binding approximation 207

4.9.4 Crystal momentum and effective electron mass 209

4.10 Other engineering applications 213

4.11 The WKB approximation 214

4.11.1 Tunneling through a high-energy barrier of finite width 215

5 Eigenstates and operators 238

5.1.1 The postulates of quantum mechanics 238

5.2 One-particle wave function space 239

5.3 Properties of linear operators 240

5.3.1 Product of operators 241

5.3.2 Properties of Hermitian operators 241

5.3.3 Normalization of eigenfunctions 243

5.3.4 Completeness of eigenfunctions 243

5.3.5 Commutator algebra 244

5.4 Dirac notation 245

5.5 Measurement of real numbers 246

5.5.1 Expectation value of an operator 247

5.5.2 Time dependence of expectation value 248

5.5.3 Uncertainty of expectation value 249

5.5.4 The generalized uncertainty relation 253

5.6 The no cloning theorem 255

5.7 Density of states 256

5.7.1 Density of electron states 256

5.7.2 Calculating density of states from a dispersion relation 263

5.7.3 Density of photon states 264

6 The harmonic oscillator 280

6.1 The harmonic oscillator potential 280

6.2 Creation and annihilation operators 282

6.2.1 The ground state of the harmonic oscillator 284

6.2.2 Excited states of the harmonic oscillator and normalization of eigenstates 287

6.3 The harmonic oscillator wave functions 291

6.3.1 The classical turning point of the harmonic oscillator 295

6.4 Time dependence 298

6.4.1 The superposition operator 300

6.4.2 Measurement of a superposition state 300

6.4.3 Time dependence of creation and annihilation operators 301

6.5 Quantization of electromagnetic fields 305

6.5.1 Laser light 306

6.5.2 Quantization of an electrical resonator 306

6.6 Quantization of lattice vibrations 307

6.7 Quantization of mechanical vibrations 308

7 Fermions and bosons 326

7.1.1 The symmetry of indistinguishable particles 327

7.2 Fermi-Dirac distribution and chemical potential 334

7.2.1 Writing a computer program to calculate the chemical potential 337

7.2.2 Writing a computer program to plot the Fermi-Dirac distribution 338

7.2.3 Fermi-Dirac distribution function and thermal equilibrium statistics 339

7.3 The Bose-Einstein distribution function 342

8 Time-dependent perturbation 353

8.1.1 An abrupt change in potential 354

8.1.2 Time-dependent change in potential 356

8.2 First-order time-dependent perturbation 359

8.2.1 Charged particle in a harmonic potential 360

8.3 Fermi's golden rule 363

8.4 Elastic scattering from ionized impurities 366

8.4.1 The coulomb potential 369

8.4.2 Linear screening of the coulomb potential 375

8.5 Photon emission due to electronic transitions 384

8.5.1 Density of optical modes in three-dimensions 384

8.5.2 Light intensity 385

8.5.3 Background photon energy density at thermal equilibrium 385

8.5.4 Fermi's golden rule for stimulated optical transitions 385

8.5.5 The Einstein A and B coefficients 387

9 The semiconductor laser 412

9.2 Spontaneous and stimulated emission 413

9.2.1 Absorption and its relation to spontaneous emission 416

9.3 Optical transitions using Fermi's golden rule 419

9.3.1 Optical gain in the presence of electron scattering 420

9.4 Designing a laser diode 422

9.4.1 The optical cavity 422

9.4.2 Mirror loss and photon lifetime 428

9.4.3 The Fabry-Perot laser diode 429

9.4.4 Semiconductor laser diode rate equations 430

9.5 Numerical method of solving rate equations 434

9.5.1 The Runge-Kutta method 435

9.5.2 Large-signal transient response 437

9.5.3 Cavity formation 438

9.6 Noise in laser diode light emission 440

9.7 Why our model works 443

10 Time-independent perturbation 450

10.2 Time-independent nondegenerate perturbation 451

10.2.1 The first-order correction 452

10.2.2 The second-order correction 453

10.2.3 Harmonic oscillator subject to perturbing potential in x 456

10.2.4 Harmonic oscillator subject to perturbing potential in x[superscript 2] 458

10.2.5 Harmonic oscillator subject to perturbing potential in x[superscript 3] 459

10.3 Time-independent degenerate perturbation 461

10.3.1 A two-fold degeneracy split by time-independent perturbation 462

10.3.2 Matrix method 462

10.3.3 The two-dimensional harmonic oscillator subject to perturbation in xy 465

10.3.4 Perturbation of two-dimensional potential with infinite barrier energy 467

11 Angular momentum and the hydrogenic atom 485

11.1 Angular momentum 485

11.1.1 Classical angular momentum 485

11.2 The angular momentum operator 487

11.2.1 Eigenvalues of angular momentum operators L[subscript z] and L[superscript 2] 489

11.2.2 Geometrical representation 491

11.2.3 Spherical coordinates and spherical harmonics 492

11.2.4 The rigid rotator 498

11.3 The hydrogen atom 499

11.3.1 Eigenstates and eigenvalues of the hydrogen atom 500

11.3.2 Hydrogenic atom wave functions 508

11.3.3 Electromagnetic radiation 509

11.3.4 Fine structure of the hydrogen atom and electron spin 515

11.4 Hybridization 516

Appendix A Physical values 532

Appendix B Coordinates, trigonometry, and mensuration 537

Appendix C Expansions, differentiation, integrals, and mathematical relations 540

Appendix D Matrices and determinants 546

Appendix E Vector calculus and Maxwell's equations 548

Appendix F The Greek alphabet 551.

Notes:

Previous ed.: 2003.

Includes index.

Includes bibliographical references and index.

ISBN:

0521860962

OCLC:

63186225

Publisher Number:

9780521860963