Quantum mechanics

Fayyazuddin, Riazuddin .Quantum mechanics (2nd Ed.,World Scientific, 2013)(ISBN 9789814412902)(T)(K)(600dpi)(562p) ......Page 3
Copyright ......Page 4
Contents xi ......Page 10
Preface vii ......Page 7
1.1 Introduction 1 ......Page 17
1.2 Breakdown of Classical Concepts 7 ......Page 23
1.3 Problems 14 ......Page 30
2.5 Stationary States 27 ......Page 33
2.2 Illustration of Heisenberg Uncertainty Principle 19 ......Page 35
2.3 Schrodinger Equation 20 ......Page 36
2.4 Physical Interpretation of Wave Function 23 ......Page 39
2.6 Eigenvalues and Eigenfunctions 29 ......Page 45
2.7 Problems 30 ......Page 46
3.1 Basic Postulates of Quantum Mechanics 33 ......Page 49
3.2 Formal Properties of Quantum Mechanical Operators 34 ......Page 50
3.3 Continuous Spectrum and Dirac Delta Functions 38 ......Page 54
3.4 Uncertainty Principle and Non-Commutativity of Observables 45 ......Page 61
3.5 Problems 48 ......Page 64
4.1 One Dimensional Potential Step 51 ......Page 67
4.2 The Potential Barrier 58 ......Page 74
4.3 Parity 61 ......Page 77
4.4 An Example of Bound State (Discrete Energy Levels)  63 ......Page 79
4.5 Bound State (Square Well Potential) 65 ......Page 81
4.6 Problems 68 ......Page 84
5.1 Introduction 71 ......Page 87
5.2 Quantum Theory of Simple Harmonic Oscillator  72 ......Page 88
5.3 Properties of Hermite Polynomial 78 ......Page 94
5.4 The Average Values 81 ......Page 97
5.5 Problems 83 ......Page 99
6.2 Properties of Angular Momentum 87 ......Page 103
6.3 Eigenfunctions and Eigenvalues of Angular Momentum 92 ......Page 108
6.4 Properties of Associated Legendre Polynomials 97 ......Page 113
6.5 Parity of a State 98 ......Page 114
6.6 Problems 99 ......Page 115
7.1 Introduction 103 ......Page 119
7.2 Coulomb Potential 106 ......Page 122
7.3 Wave Functions of Hydrogen-like Atom 110 ......Page 126
7.4 Problems 114 ......Page 130
8.1 Two Body Problem: (Centre of Mass Motion) 117 ......Page 133
8.2 Collision Theory 120 ......Page 136
8.3 Kinematices of a Scattering Process 121 ......Page 137
8.4 Scattering Cross Section 125 ......Page 141
8.5 Scattering by a Spherical Symmetry Potential 127 ......Page 143
8.6 Phase Shifts 131 ......Page 147
8.7 Optical Theorem 136 ......Page 152
8.8 Resonances, Dispersion Formula 141 ......Page 157
8.9 Bound States and Resonances: Square Well Potential . 144 ......Page 160
8.10 5-function Potential 147 ......Page 163
8.11 The Born Approximation . 150 ......Page 166
8.12 Quasi-Classical Approximation 157 ......Page 173
8.13 Problems 168 ......Page 184
9.1 State Vectors 173 ......Page 189
9.2 Schrodinger Representation 179 ......Page 195
9.3 Relation between the Momentum and Schrodinger Representations 183 ......Page 199
9.4 Matrix Mechanics 185 ......Page 201
9.5 Simple Harmonic Oscillator 188 ......Page 204
9.6 Supersymmetric Oscillator 192 ......Page 208
9.7 Problems 193 ......Page 209
10.1 Introduction 199 ......Page 215
10.2 Heisenberg Equation of Motion 201 ......Page 217
10.3 Free Particle Propagator 205 ......Page 221
10.4 Unitary Transformation 207 ......Page 223
10.5 Invariance Principles, Coservation Laws 209 ......Page 225
10.6 Discrete Transformation 216 ......Page 232
10.7.1 Introduction 219 ......Page 235
10.7.2 Path Integral Method 220 ......Page 236
10.7.3 Free Particle Propagator from Path Integral Formulism 223 ......Page 239
10.7.4 Motion with a Source: Generating Functional for Time-ordered Products of Heisenberg Operators qi(t) 224 ......Page 240
10.8 Problems 230 ......Page 246
11.1 The Zeeman Effect 235 ......Page 251
11.2 Angular Momentum 238 ......Page 254
11.3 Matrix Representation of Angular Momentum 242 ......Page 258
11.4 Spin 244 ......Page 260
11.5 Splitting of the Ground State of Hydrogen Atom 248 ......Page 264
11.6 Addition of Spin 249 ......Page 265
11.7 Addition of Angular Momenta 252 ......Page 268
11.8 Rotations: Rotation Matrices 259 ......Page 275
11.9 Vector and Tensor Operators 266 ......Page 282
11.10a Wigner-Eckart Theorem 270 ......Page 286
11.10b Application of Wigner-Eckart Theorem 272 ......Page 288
11.11 Problems 274 ......Page 290
12.2 Stationary Perturbation Theory 281 ......Page 297
12.3 Degeneracy 285 ......Page 301
12.4 The Stark Effect 288 ......Page 304
12.5 Non-Perturbative Method (Variational Principle) 293 ......Page 309
12.6 Problems 297 ......Page 313
13.1 Transition Probability 301 ......Page 317
13.2 Problems 307 ......Page 323
14.1 Introduction 309 ......Page 325
14.2 Permutation Operator and Exclusion Principle 310 ......Page 326
14.3 Non-interacting Particles and Exclusion Principle  312 ......Page 328
14.4 Two Electrons System (Helium Atom) 314 ......Page 330
14.5 Scattering of Identical Particles 317 ......Page 333
14.6 Problems 319 ......Page 335
15.1 Introduction 323 ......Page 339
15.2 Magnetic Spin Resonance 327 ......Page 343
15.3.1 Introduction 330 ......Page 346
15.3.2 General Formalism for Particle Mixing  332 ......Page 348
15.3.3 K° -K° Complex 335 ......Page 351
15.3.4 Complex (q = d,s) 337 ......Page 353
15.3.5 Neutrino Oscillations 338 ......Page 354
15.4 Problems 342 ......Page 358
16.1 Introduction 343 ......Page 359
16.2 Qubit 344 ......Page 360
16.3 Multiple Qubit Systems 345 ......Page 361
16.4 Matrix Representation of Qubits 346 ......Page 362
16.5 Single Qubit Logic Gates 347 ......Page 363
16.7 Two Qubit Logic Gates 349 ......Page 365
16.8 Quantum Circuits 351 ......Page 367
16.9 EPR Entanglement 352 ......Page 368
16.10 Problems 354 ......Page 370
17.1 Interaction of Electromagnetic Field with Electrons  357 ......Page 373
17.2 Gauge Principle: Aharanov-Bohm Effect 360 ......Page 376
17.3 Landau Levels 365 ......Page 381
17.4 Quantization of Radiation Field 367 ......Page 383
17.5 Perturbation Induced by Electromagnetic Field  371 ......Page 387
17.6 Stimulated Emission and Absorption of Radiation  372 ......Page 388
17.7 Spontaneous Emission of Radiation: Dipole Approximation 376 ......Page 392
17.8.1 Ei Transition 381 ......Page 397
17.8.2 Magnetic Dipole Transition due to Intrinsic Spin 384 ......Page 400
17.9 Dipole Sum Rules, Two Point Function 385 ......Page 401
17.10 Application of Dipole Sum Rules 390 ......Page 406
17.11 Dispersion Relation 392 ......Page 408
17.12 Problems 394 ......Page 410
18.1 Introduction 401 ......Page 417
18.2 Interaction Picture 403 ......Page 419
18.3 Formal Solution of Schrodinger Equation in the Interaction Picture 405 ......Page 421
18.4 Scattering States — The S-Matrix 410 ......Page 426
18.5 The Scattering Cross-section 416 ......Page 432
18.6 Properties of the Scattering States 418 ......Page 434
18.7 The Coordinate Representation 420 ......Page 436
18.8 Unitarity of the 5-Matrix 426 ......Page 442
18.9 Optical Theorem 429 ......Page 445
18.10 Problems 430 ......Page 446
19.1 Introduction 433 ......Page 449
19.2 Rotational Invariance 435 ......Page 451
19.3 Parity 440 ......Page 456
19.4 Time Reversal 443 ......Page 459
19.5 Problems 448 ......Page 464
20.1 A Brief Review of the Theory of Relativity 449 ......Page 465
20.2 Relativistic Quantum Mechanics: Introduction 454 ......Page 470
20.3 Dirac Equation 456 ......Page 471
20.4 Covariant Form of Dirac Equation 459 ......Page 475
20.5 Relativistic Invariance of Dirac Equation 462 ......Page 478
20.6 Transformation Properties of Dirac Bilinears 466 ......Page 482
20.7 Discrete Transformations 468 ......Page 484
20.8.1 Matrix Representation of the Generators of the Lorentz Group 473 ......Page 489
20.8.2 Representations of Lorentz Group 475 ......Page 491
20.9 Gauge Invariance: Dirac Equation in the Presence of Electromagnetic Field 479 ......Page 495
20.10 Constants of Motion 481 ......Page 497
20.11 ‘Velocity’ in Dirac Theory 484 ......Page 500
20.12 Two Component Pauli Form of Dirac Equation: Existence of Magnetic Moment 486 ......Page 502
20.13 Dirac Equation for the Hydrogen-like Atom 489 ......Page 505
20.14 Hole Theory and Existence of Positrons (Anti-matter) 494 ......Page 510
20.15 Free Particle Solutions, Plane Wave Solutions of Dirac Equation 495 ......Page 511
20.16 Charge Conjugation 502 ......Page 518
20.17 Large and Small Bilinear Covariants 504 ......Page 520
20.18 Weyl Equation 506 ......Page 522
20.19 Problems 508 ......Page 524
21.1 Dirac Equation in (1+2) Dimensions 513 ......Page 529
21.1.1 Dirac Equation in Hamiltonian Form and Plane Wave Solutions 515 ......Page 531
21.2.1 Introduction 517 ......Page 533
21.2.2 Electronic Properties of Graphene 518 ......Page 534
21.2.3 Cyclotron Mass 523 ......Page 539
21.2.4 Dirac Hamiltonian and Dirac Equation for Quasiparticles in Graphene 524 ......Page 540
21.2.5 Tunneling and Klein Paradox 526 ......Page 542
21.2.6 Dirac Fermions in an External Gauge Field (Electromagnetic): Landau Levels 529 ......Page 545
21.3 Problems 533 ......Page 549
21.4 Selected References and Further Reading 534 ......Page 550
Index 537 ......Page 553
cover ......Page 1
back cover......Page 562