An Introduction To Quantum Physics

Description

An Introduction To Quantum Physics......Page 1 Half Title......Page 2 Title Page......Page 4 Copyright Page......Page 5 Table of Contents......Page 6 Preface......Page 12 Learning Aids For Quantum Physics......Page 16 1-1 Introduction......Page 22 1-2 The classical atom......Page 25 1-3 The electrical structure of matter......Page 26 1-4 The Thomson atom......Page 32 1-5 Line spectra......Page 35 1-6 Photons......Page 38 1-7 The Rutherford-Bohr atom......Page 45 1-8 Further predictions of the Bohr model......Page 50 1-9 Direct evidence of discrete energy levels......Page 51 I-10 X-ray spectra......Page 54 1-11 A note on x-ray spectroscopy......Page 60 1-12 Concluding remarks......Page 64 EXERCISES......Page 66 2-1 De Broglie's hypothesis......Page 76 2-2 De Broglie waves and particle velocities......Page 79 2-3 Calculated magnitudes of De Broglie wavelengths......Page 83 2-4 The Davisson-Germer experiments......Page 85 2-5 More about the Davisson-G ermer experiments......Page 89 2-6 Further manifestations of the wave properties electrons......Page 93 2-7 Wave properties of neutral atoms and molecules......Page 99 2-8 Wave properties of nuclear particles......Page 103 2-9 The meaning of the wave-particle duality......Page 106 2-10 The coexistence of wave and particle properties......Page 108 2-11 A first discussion of quantum amplitudes......Page 114 EXERCISES......Page 116 3-1 Preliminary remarks......Page 126 3-2 The approach to a particle-wave equation......Page 128 3-3 The Schrodinger equation......Page 130 3-4 Stationary states......Page 133 3-5 Particle in a one-dimensional box......Page 134 3-6 Unique energy without unique momentum......Page 138 3-7 Interpretation of the quantum amplitudes for bound states......Page 140 3-8 Particles in nonrigid boxes......Page 144 3-9 Square well of finite depth......Page 148 3-10 Normalization of the wave function......Page 150 3-11 Qualitative plots of bound-state wave functions......Page 152 EXERCISES......Page 166 4-1 Introduction......Page 176 4-2 The square well......Page 177 4-3 The harmonic oscillator......Page 183 4-4 Vibrational energies of diatomic molecules......Page 191 4-5 Computer solutions of the Schrödinger equation......Page 195 EXERCISES......Page 205 5-2 The three-dimensional Schrödinger equation......Page 214 5-3 Eigenfunctions and eigenvalues......Page 216 5-4 Particle in a three-dimensional box......Page 217 5-5 Spherically symmetric solutions for hydrogen-like systems......Page 220 5-6 Normalization and probability densities......Page 229 5-7 Expectation values......Page 232 5-8 Computer solutions for spherically symmetric wave functions......Page 237 EXERCISES......Page 242 6-1 Introduction......Page 252 6-2 States of linear polarization......Page 254 6-3 Linearly polarized photons......Page 258 6-4 Probability and the behavior of polarized photons......Page 262 6-5 States of circular polarization......Page 264 6-6 Orthogonality and completeness......Page 267 6-7 Quantum states......Page 271 6-8 Statistical and classical properties of light......Page 274 6-9 Concluding remarks......Page 275 6A-1 The production of linearly polarized light......Page 277 6A-2 The production of circularly polarized light......Page 282 Suggested experiments with linearly polarized light......Page 287 EXERCISES......Page 291 7-1 Introduction......Page 300 7-2 The analyzer loop......Page 301 7-3 Paradox of the recombined beams......Page 304 7-4 Interference effect in general......Page 306 7-5 Formalism of projection amplitudes......Page 309 7-6 Properties of projection amplitudes......Page 311 7-7 Projection amplitudes for states of polarization......Page 315 7-8 The state vector......Page 319 7-9 The state vector and the Schrodinger wave function for bound states......Page 325 EXERCISES......Page 327 8-1 Introduction......Page 336 8-2 Superposition of states......Page 337 8-3 An example of motion in a box......Page 338 8-4 Packet states in a square-well potential......Page 342 8-5 The position-momentum uncertainty relation......Page 348 8-6 The uncertainty principle and ground-state energies......Page 351 8-7 Free-particle packet states......Page 352 8-8 Packet states for moving particles......Page 357 8-9 Examples of moving packet states......Page 359 8-10 The energy-time uncertainty relation......Page 364 8-11 Examples of the energy-time uncertainty relation......Page 366 8-12 The shape and width of energy levels......Page 372 EXERCISES......Page 375 9-1 Scattering processes in terms of wave packets......Page 388 9-2 Time-independent approach to phenomena......Page 390 9-3 Probability density and probability current......Page 395 9-4 Scattering by a one-dimensional well......Page 400 9-5 Barrier penetration: tunneling......Page 404 9-6 Probability current and barrier penetration problems......Page 410 9-7 An approximation for barrier penetration calculations......Page 413 9-8 Field emission of electrons......Page 416 9-9 Spherically symmetric probability currents......Page 420 9-10 Quantitative theory of alpha decay......Page 424 9-11 Scattering of wave packets......Page 429 EXERCISES......Page 435 10-1 Introduction......Page 446 10-2 Stern-Gerlach experiment: theory......Page 449 10-3 Stern-Gerlach experiment: descriptive......Page 453 10-4 Magnitudes of atomic dipole moments......Page 459 10-5 Orbital angular momentum operators......Page 463 10-6 Eigenvalues of Lz......Page 466 10-7 Simultaneous eigenvalues......Page 470 10-8 Quantum states of a two-dimensional harmonic oscillator......Page 475 EXERCISES......Page 484 11-2 Total orbital angular momentum in central fields......Page 494 11-3 Rotational states of molecules......Page 508 11-4 Spin angular momentum......Page 521 11-5 Spin orbit coupling energy......Page 523 11-6 Formalism for total angular momentum......Page 526 APPENDIX: THE SCHRÖDINGER EQUATION IN SPHERICAL COORDINATES......Page 527 EXERCISES......Page 530 12-2 The Coulomb model......Page 540 12-3 General features of the radial wave functions for hydrogen......Page 544 12-4 Exact radial wave functions for hydrogen......Page 549 12-5 Complete Coulomb wave functions......Page 552 12-6 Classification of energy eigenstates in hydrogen......Page 558 12-7 Spectroscopic notation......Page 560 12-8 Fine structure of hydrogen energy levels......Page 561 12-9 Isotopic fine structure: heavy hydrogen......Page 565 12-10 Other hydrogen-like systems......Page 567 EXERCISES......Page 571 13-1 Introduction......Page 578 13-2 Schrôdinger's equation for two noninteracting particles......Page 579 13-3 The consequences of identity......Page 582 13-4 Spin states for two particles......Page 585 13-5 Exchange symmetry and the Pauli principle......Page 587 13-6 When does symmetry or antisymmetry matter?......Page 590 13-7 Measurability of the symmetry character......Page 592 13-8 States of the helium atom......Page 596 13-9 Many-electron atoms......Page 608 13-10 General structure of a massive atom......Page 616 EXERCISES......Page 619 14-2 The classical Hertzian dipole......Page 626 14-3 Radiation from an arbitrary charge distribution......Page 629 14-4 Radiating dipoles according to wave mechanics......Page 633 14-5 Radiation rates and atomic lifetimes......Page 636 14-6 Selection rules and radiation patterns......Page 638 14-7 Systematics of line spectra......Page 647 14-8 Angular momentum of photons......Page 649 14-9 Magnetic dipole radiation and galactic hydrogen......Page 652 14-10 Concluding remarks......Page 658 EXERCISES......Page 659 Bibliography......Page 673 Answers To Exercises......Page 666 Selected Physical Constants And Conversion Factors......Page 682 Index......Page 684 Back Cover......Page 693