Robert eisberg, robert resnick quantum physics of atoms, molecules, solids, nuclei, and particles wiley (1985)

Useful Constants and Conversion Factors Quoted to a useful number of significant figures Speed of light in vacuum Electron charge magnitude Planck's constant Boltzmann's constant Avogadro's number Coulomb's law constant c = 2.998 x 108 m/sec e = 1.602 x = 19 coul h = 6.626 x 10 -34 joule-sec h = h /27c = 1.055 x 10 -34 joule-sec = 0.6582 x 10 -15 eV-sec k = 1.381 x 10 -23 joule / °K = 8.617 x 10 -5 eV/ °K No = 6.023 x 1023/mole /47rE0 = 8.988 x 109 nt - m2 /coul2 Electron rest mass me = 9.109 x 10 -31 kg = 0.5110 MeV/c p = 1.672 x 10 -27 kg = 938.3 MeV/c2 m Proton rest mass Neutron rest mass m„ = 1.675 x 10 -Z7 kg = 939.6 MeV/c Atomic mass unit (C 12 = 12) -27 kg = 931.5 MeV/c u=1.6x0 ub = eh/2me = 9.27 x 10 -24 amp-m2 (or joule/tesla) µn = eh/2m, = 5.05 x 10 -27 amp-m2 (or joule /tesla) ao = 47c€0h2/mee2 = 5.29 x 10 -11 m = 0.529 A E1 = — mee 4/(4rcE0)22h2 = —2.17 x 10 -18 joule = —13.6 eV Electron Compton wavelength Ac = h/mec = 2.43 x 10 -12 m = 0.0243 A Fine-structure constant a = e2 /4nE 0hc = 7.30 x 10 -3 1/137 kT at room temperature k300 °K = 0.0258 eV ^ 1/40 eV Bohr magneton Nuclear magneton Bohr radius Bohr energy 1eV= 1.602 x 10 -19 joule A=10 -10 m 1F=10 -15 m i joule = 6.242 x 10 18 eV l barn (bn)= 10-28m2 QUANTUM PHYSICS Assisted by yid O CaIgweal Univer^^#y^qf^#^rni^ ^^ arbara United'•°Stalês C^^t^^ ^,;^^ Odemy figure on the cover is frori ; èction 9-4, where it is used to show the tendency for two identical spin 1/2 particles (such as electrons) to avoid each other if their spins are essentially parallel This tendency, or its inverse for the antiparallel case, is one of the recurring themes in quantum physics explanations of the properties of atoms, molecules, solids, nuclei, and particles The „ QUANTUM PHYSICS of Atoms, Molecules, Solids, Nuclei, and Particles Second Edition ROBERT EISBERG University of California, Santa Barbara JOHN WILEY & SONS New York Chichester Brisbane Toronto Singapore Copyright © 1974, 1985, by John Wiley & Sons, Inc All rights reserved Published simultaneously in Canada Reproduction or translation of any part of this work beyond that permitted by Sections 107 and 108 of the 1976 United States Copyright Act without the permission of the copyright owner is unlawful Requests for permission or further information should be addressed to the Permissions Department, John Wiley & Sons Library of Congress Cataloging in Publication Data: Eisberg, Robert Martin Quantum physics of atoms, molecules, solids, nuclei, and particles Includes index Quantum theory I Resnick, Robert, 1923— II Title, QC174.12.E34 1985 ISBN 0-471-87373-X 530.1'2 84-10444 Printed in the United States of America Printed an d bound by the Hamilton Printing Comp any 30 29 28 27 26 25 24 23 PREFACE TO THE SECOND EDITION The many developments that have occurred in the physics of quantum systems since the publication of the first edition of this book—particularly in the field of elementary particles—have made apparent the need for a second edition In preparing it, we solicited suggestions from the instructors that we knew to be using the book in their courses (and also from some that we knew were not, in order to determine their objections to the book) The wide acceptance of the first edition made it possible for us to obtain a broad sampling of thought concerning ways to make the second edition more useful We were not able to act on all the suggestions that were received, because some were in conflict with others or were impossible to carry out for technical reasons But we certainly did respond to the general consensus of these suggestions Many users of the first edition felt that new topics, typically more sophisticated aspects of quantum mechanics such as perturbation theory, should be added to the book Yet others said that the level of the first edition was well suited to the course they teach and that it should not be changed We decided to try to satisfy both groups by adding material to the new edition in the form of new appendices, but to it in such a way as to maintain the decoupling of the appendices and the text that characterized the original edition The more advanced appendices are well integrated in the text but it is a one-way, not two-way, integration A student reading one of these appendices will find numerous references to places in the text where the development is motivated and where its results are used On the other hand, a student who does not read the appendix because he is in a lower level course will not be frustrated by many references in the text to material contained in an appendix he does not use Instead, he will find only one or two brief parenthetical statements in the text advising him of the existence of an optional appendix that has a bearing on the subject dealt with in the text The appendices in the second edition that are new or are significantly changed are: Appendix A, The Special Theory of Relativity (a number of worked-out examples added and an important calculation simplified); Appendix D, Fourier Integral Description of a Wave Group (new); Appendix G, Numerical Solution of the TimeIndependent Schroedinger Equation for a Square Well Potential (completely rewritten to include a universal program in BASIC for solving second-order differential equations on microcomputers); Appendix J, Time-Independent Perturbation Theory (new); Appendix K, Time-Dependent Perturbation Theory (new); Appendix L, The Born Approximation (new); Appendix N, Series Solutions of the Angular and Radial Equations for a One-Electron Atom (new); Appendix Q, Crystallography (new); Appendix R, Gauge Invariance in Classical and Quantum Mechanical Electromagnetism (new) Problem sets have been added to the ends of many of the appendices, both old and new In particular, Appendix A now contains a brief but comprehensive set of problems for use by instructors who begin their "modern physics" course with a treatment of relativity v PREFA CE TO THE S ECO ND EDITIO N A large number of small changes and additions have been made to the text to improve and update it There are also several quite substantial pieces of new material, including: the new Section 13-8 on electron-positron annihilation in solids; the additions to Section 16-6 on the Mössbauer effect; the extensive modernization of the last half of the introduction to elementary particles in Chapter 17; and the entirely new Chapter 18 treating the developments that have occurred in particle physics since the first edition was written We were very fortunate to have secured the services of Professor David Caldwell of the University of California, Santa Barbara, to write the new material in Chapters 17 and 18, as well as Appendix R Only a person who has been totally immersed in research in particle physics could have done what had to be done to produce a brief but understandable treatment of what has happened in that field in recent years Furthermore, since Caldwell is a colleague of the senior author, it was easy to have the interaction required to be sure that this new material was closely integrated into the earlier parts of the book, both in style and in content Prepublication reviews have made it clear that Caldwell's material is a very strong addition to the book Professor Richard Christman, of the U.S Coast Guard Academy, wrote the new material in Section 13-8, Section 16-6, and Appendix Q, receiving significant input from the authors We are very pleased with the results The answers to selected problems, found in Appendix S, were prepared by Professor Edward Derringh, of the Wentworth Institute of Technology He also edited the new additions to the problem sets and prepared a manual giving detailed solutions to most of the problems The solutions manual is available to instructors from the publisher It is a pleasure to express our deep appreciation to the people mentioned above We also thank Frank T Avignone, III, University of South Carolina; Edward Cecil, Colorado School of Mines; L Edward Millet, California State University, Chico; and James T Tough, The Ohio State University, for their very useful prepublication reviews The following people offered suggestions or comments which helped in the development of the second edition: Alan H Barrett, Massachusetts Institute of Technology; Richard H Behrman, Swarthmore College; George F Bertsch, Michigan State University; Richard N Boyd, The Ohio State University; Philip A Casabella, Rensselaer Polytechnic Institute; C Dewey Cooper, University of Georgia; James E Draper, University of California at Davis; Arnold Engler, Carnegie-Mellon University; A T Fromhold, Jr., Auburn University; Ross Garrett, University of Auckland; Russell Hobbie, University of Minnesota; Bei-Lok Hu, University of Maryland; Hillard Huntington, Rensselaer Polytechnic Institute; Mario Iona, University of Denver; Ronald G Johnson, Trent University; A L Laskar, Clemson University; Charles W Leming, Henderson State University; Luc Leplae, University of Wisconsin-Milwaukee; Ralph D Meeker, Illinois Benedictine College; Roger N Metz, Colby College; Ichiro Miyagawa, University of Alabama; J A Moore, Brock University; John J O'Dwyer, State University of New York at Oswego; Douglas M Potter, Rutgers State University; Russell A Schaffer, Lehigh University; John W Watson, Kent State University; and Robert White, University of Auckland We appreciate their contribution Santa Barbara, California Troy, New York Robert Eisberg Robert Resnick PREFACE TO THE FIRST EDITION The basic purpose of this book is to present clear and valid treatments of the properties of almost all of the important quantum systems from the point of view of elementary quantum mechanics Only as much quantum mechanics is developed as is required to accomplish the purpose Thus we have chosen to emphasize the applications of the theory more than the theory itself In so doing we hope that the book will be well adapted to the attitudes of contemporary students in a terminal course on the phenomena of quantum physics As students obtain an insight into the tremendous explanatory power of quantum mechanics, they should be motivated to learn more about the theory Hence we hope that the book will be equally well adapted to a course that is to be followed by a more advanced course in formal quantum mechanics The book is intended primarily to be used in a one year course for students who have been through substantial treatments of elementary differential and integral calculus and of calculus level elementary classical physics But it can also be used in shorter courses Chapters through introduce the various phenomena of early quantum physics and develop the essential ideas of the old quantum theory These chapters can be gone through fairly rapidly, particularly for students who have had some prior exposure to quantum physics The basic core of quantum mechanics, and its application to one- and two-electron atoms, is contained in Chapters through and the first four sections of Chapter This core can be covered well in appreciably less than half a year Thus the instructor can construct a variety of shorter courses by adding to the core material from the chapters covering the essentially independent topics: multielectron atoms and molecules, quantum statistics and solids, nuclei and particles Instructors who require a similar but more extensive and higher level treatment of quantum mechanics, and who can accept a much more restricted coverage of the applications of the theory, may want to use Fundamentals of Modern Physics by Robert Eisberg (John Wiley & Sons, 1961), instead of this book For instructors requiring a more comprehensive treatment of special relativity than is given in Appendix A, but similar in level and pedagogic style to this book, we recommend using in addition Introduction to Special Relativity by Robert Resnick (John Wiley & Sons, 1968) Successive preliminary editions of this book were developed by us through a procedure involving intensive classroom testing in our home institutions and four other schools Robert Eisberg then completed the writing by significantly revising and extending the last preliminary edition He is consequently the senior author of this book Robert Resnick has taken the lead in developing and revising the last preliminary edition so as to prepare the manuscript for a modern physics counterpart at a somewhat lower level He will consequently be that book's senior author The pedagogic features of the book, some of which are not usually found in books at this level, were proven in the classroom testing to be very suỗcessful These features are: detailed outlines at the beginning of each chapter, numerous worked out vii PREFACE TO THE FIRS T EDITIO N examples in each chapter, optional sections in the chapters and optional appendices, summary sections and tables, sets of questions at the end of each chapter, and long and varied sets of thoroughly tested problems at the end of each chapter, with subsets of answers at the end of the book The writing is careful and expansive Hence we believe that the book is well suited to self-learning and to self-paced courses We have employed the MKS (or SI) system of units, but not slavishly so Where general practice in a particular field involves the use of alternative units, they are used here It is a pleasure to express our appreciation to Drs Harriet Forster, Russell Hobbie, Stuart Meyer, Gerhard Salinger, and Paul Yergin for constructive reviews, to Dr David Swedlow for assistance with the evaluation and solutions of the problems, to Dr Benjamin Chi for assistance with the figures, to Mr Donald Deneck for editorial and other assistance, and to Mrs Cassie Young and Mrs Carolyn Clemente for typing and other secretarial services Santa Barbara, California Troy, New York Robert Eisberg Robert Resnick N Box normalization, 182 Brackett series, 98 Bragg scattering condition, 58, 459 Bravais lattice, Q-2 Breeder reactor, 606 Breit- Wigner formula, 596 Bremsstrahlung, 42 Brillouin zone, 460 Broken symmetry, 674 Brueckner theory, 529 Control rod, 606 Cooper pair, 487, 546 Copenhagen interpretation, 79 Correlation angle, 465 Correspondence principle, 117 Cosmic rays, 42, 44 Coulomb potential, 234 screened, L-7 Coulomb scattering, 90, 591, E-1 cross section for, 95 Coulomb term, 527 Coupling constant, 682 beta, 569, 573 electromagnetic, 639 nuclear, 638 Covalent bond, 418 Covalent solid, 444 CP operation, 657 CPT theorem, 658 Critical field, 485 Critical temperature, 484 Cross section, 48 Compton scattering, 49 Coulomb scattering, 95 pair production, 49 photoelectric, 49 total photon, 49 Crystal lattice, 443 Crystallography, 448, Q-1 Curie law, 494 Curie temperature, 497 ferromagnetic, 497 Curve of stability, 563 Cabibbo angle, 703 Carbon atom, energy levels of, 361 Carbon cycle, 610 Cascade hyperon, 649 Causality and qu antum theory, 79, 139 Cavity radiation; see Blackbody radiation Centrifugal potential, 345, 536 Chain reaction, 602 Charge conjugation, 655 Charge density: atomic, 323 nuclear, 516 Charge independence, 618, 621 Charm, 678 quantum number, 678 Charmonium, 680 Classical limit for orbital angular momentum, 259 of quantum theory, 117, 184 for simple harmonic oscillator, 21, 136, 165 for step potential, 198 Classically excluded region, 213 Collective model, 545, 549 Color, 683 Daughter nucleus, 556 Color charge, 684, 699 Davisson-Germer experiment, 57 Color force field, 686 De Broglie postulate, 56 Comparative lifetime, 571 and Bohr quantization postulate, 112 Complementarity principle, 63 and infmite square well, 218 Complex conjugate, 135, F-1 and Schroedinger equation, 129 Complex exponential, F-2 and uncertainty principle, 72 Complex number, F-1 De Broglie wave, 56, 69 and Schroedinger equation, 134 De Broglie wavelength, 56 Compound nucleus, 591, 595 Debye specific heat theory, 389 Compound nucleus resonance, 595 Debye temperature, 390 Compton effect, 34 Decay energy: theory of, 36 alpha, 556 and uncertainty principle, 68 beta, 564 Compton scattering cross section, 49 Decay law, 558 Compton shift, 35, 37 Decay rate, 558 Compton wavelength, 37 alpha, 207 Conduction band, 450 beta, 570 Conduction electron, 32, 191, 215, 405 gamma, 579 Conductivity, 450, 463 Deep-inelastic scattering, 669 Conductors, 449 Degeneracy, 115, 239, 240, 327 Configuration, 332 of atomic eigenfunctions in applied field, Conse rvation laws: 252 for nuclear reactions, 588 for Coulomb potential, 536 for observed interactions, 654 exchange, 305 Contact potential, 27, 407 perturbation theory of, J-8 Continuity of eigenfunction and derivative, 155, Degeneracy effect for gases, 401 214 Delayed neutron emission, 606 Continuum energy states, 110 Delta particle, 651 and Schroedinger theory, 163 Density of states, in band, 455 Contraction, Lorentz, A-8 and effective mass, 463 for free particle, 453 for photons, 398 Detailed balancing, 381, 639 Deuterium, 107 Deuteron, 619 Diamagnetism, 493 Differential cross section, 94, L-4 Differential equation, 127 Differential operator, 144 Diffraction: general formula for, 57 of particles, 58, 76 an d uncertainty principle, 67, 77 Dilation, time, A-8 Dirac theory: and beta decay, 566 and hydrogen energy levels, 286 an d pair production, 47 and Schroedinger theory, 132 Direct interaction, 591, 593 Directional bond, 422 Distance of closest approach, 91 Dist ribution function, See also specific types D meson, 679 Domains, 500 Donor impurities, 468 Doping, 467 Doppler shift and Mdssbauer effect, 586 relativistic, 46 D rift speed, 450 Dual nature of radiation, see Wave-particle duality Dulong-Petit law, 388 Dynamical quantity, 143 Effective mass, in crystal lattice, 461 in nuclei, 533 Effective Z, 325 Eigenfunction, 154, 166, 242, 262 degenerate, J-8 required properties of, 155 Eigenvalue, 165, 239, 262 Eigenvalue equation, 259, 262 Einstein A and B coefficients, 394, 395 Einstein photon hypothesis, 30, 63 Einstein relativity postulate, A-5 Einstein specific heat theory, 388 Elastic scattering, 593, 668 Electric dipole radiation, B-3 Electric dipole tran sition, 289, 580 Electric quadrupole moment, 514, 546, 600 Electromagnetic interaction, 574, 653, 655 Electromagnetic spectrum, 33 Electron, 59 Electron affinity, 336 Electron capture, 564 Electron emission, 564 Electron gas, 404, 406 Electron molecular spectra, 429 Electronic neut ri no, 642 Electronic specific heat, 406 Electron-positron an nihilation, 464 Electron-positron pair, 43 Electron radius, 277 Electron spin resonance, 369 Electron volt unit, 29 Electroweak gauge theory, 699, 701 Elements: abundances of, 510 origin of, 607 periodic table of, 330 Emission: spontaneous, 291, 393 stimulated, 291, 393 Emission spectrum, 98 Emissivity, End point, 565 Energy b an d, 446 Energy gap, 489 Energy level diagram, 20 x-ray, 339 Energy quantization: of one-electron atom, 101 Pl an ck postulate of, 14 of radiation, 30 in Schroedinger theory, 157 an d uncertainty principle, 68 by Wilson-Sommerfeld rules, 110 Enhancement factor, 380 Entropy, 410 Equilibrium decay, 559 Equipartition of energy, 12 Eta meson, 651 Ether frame, A-3 Even function, 140 Exchange: of particle lables, 306 of phonons, 487 of pions, 634 Exchange degeneracy, 305 Exchange force, 316 Exchange interaction, 498 Exchange operator, 624 Excited state, 102 Exclusion principle, 308, 319 an d atomic structure, 337 in LS coupling, 363, P-1 an d nuclear structure, 531 Exhaustion region, 481 Expectation value, 141 general presc ri ption for, 146, 171 Exponential attenuation, 50 Exponential decay law, 558 Extrinsic conductivity, 467 Extrinsic region, 481 Fermi distribution, 383, 384 Fermi energy, 385 for metals, 406 for nucleus, 531 in semiconductors, 471 Fermi gas, 405 Fermi gas model, 531, 549 Fermi momentum, 465, 480, 671 Fermion, 310, 378, 382 Fermi selection rules, 571 Fermi temperature, 480 X W — Fermi unit, 94, 511 Fermi velocity, 479 Fermi-Yang model, 673 Ferrimagnetism, 503 Ferromagnetism, 493, 497 Feynman dia gr am, 669 Filled subshell, 252, 363 Fine stru cture, 114, 276 in hydrogen atom, 287 Landé interval rule for, 359 Fine structure const an t, 116, 286, 639, 682 Finiteness of eigenfunction and derivative, 155 Fission, 525, 602 Fission fragment, 602 Flavors, 678 Flux, probability, 196 Flux quantization, 491 Fock calculation, 322 Forbidden b an d, 447 Forbidden beta decay, 572 Forward bias, 473 Fourier integral, D-1 Franck-Condon principle, 432 Fr an ck-He rt z experiment, 107 Free electron gas, 404 Free electron model, 452 Free particle: density of states for, 453 qu antum mechanical behavior of, 178 Frustrated total internal reflection, 205 FT value, 571 Fundamental tran slation vectors, Q-1 Fusion, 525 Fusion reactor, 607 Galilean tr an sformation, A-1 Gamma decay, 578 selection rules for, 580 tr an sition rate, 79 Gamma ray, 32, 578 Gamow- Teller selection rules, 572 Gas degeneration, 401 Gauge fields, 691 Gauge inva rian ce, 655, R-1 Gauge inva rian t, 689 Gauge theories, 688 Gauge tran sformation, R-1 Gaussian dist ri bution, D-3 Gaussian potential, L-7 Geiger-Marsden experiment, 89 Gell-Mann-Nishijima relation, 646, 681 Generation, quark-lepton, 705 g factor, Landé, 368 orbital, 269 spin, 274 GIM mechanism, 704 Global gauge symmetry, 688 Glueballs, 692 Gluons, 684, 692 mass of, 697 Golden Rule No 2, K-5 Goldstone boson, 701 Goudsmit- Uhlenbeck postulate, 276 Gr an d unification theories, 706 Gravitational interaction, 574, 654 Gravitational red shift, 588 Graviton, 654 Ground state, 102 Group velocity, 72 Group wave function, 182, 192 Group of waves, 70 Hadron, 649 Half-life, 559 Hall coefficient, 451, 479 Hall effect, 451 Halogen, 336 Hamiltonian, 262 Handedness, see Helicity Harmonic oscillator, see Simple harmonic oscillator Hartree theory, 319 Heat capacity, 388 Heisenberg matrix mechanics, 261 Heisenberg principle, see Uncertainty principle Helicity, 577, 642, 657 Helium energy levels, 317 Hermite polynomials, I-5 Heteropolar bond, 418 Heusler alloy, 499 Hidden va ri ables, 79 Hierarchy problem, 708 Higgs particles, 702 Hole, 451 in filled band, 464 an d positron, 47 an d x-ray spec tr a, 338 Homopolar bond, 422 Hydrogen energy levels, 101, 286 Hydrogen molecular ion, 418 Hypercharge, 674 Hyperfine splitting, 288, 363, 512 Hyperon, 648 Hysterisis, 501 Identical particles, 302 Imaginary number, 131, F-1 Imaginary pa rt, F-1 Impact parameter, 90 Independent particle motion: in atoms, 320 in nuclei, 531 Indeterminacy principle, see Uncertainty principle Indicial equation, N-4 Indistinguishability, 303 and qu an tum statistics, 377 Induced fission, 603 Inelastic scattering, 593 Inertial frame, A-2 Infmite square well potential, 214 ground state of, 147 Inhibition factor, 378 Insulator, 448 Interactions, comparison of properties, 574, 653 Interatomic force, 416 Intermediate boson, 643, 653 Internal conversion, 581 coefficient of, 582 Intensity, of radiation, 63 Interval rule, 359 in hyperfine splitting, 514 Intrinsic conductivity, 467 Intrinsic parity, 639 Inversion of NH3, 209 Ionic bond, 416 Ionization energy, 110, 335, 336 Irreducible, 674 Isobar, 601, 632 Isobaric an alogue levels, 633 Isolated band, 448, 449 Isomer shi ft , 587 Isospin, 631 Isotope, 521 Isotope effect, 486 Isotopic abundance, 428, 437 Isotopic spin, see Isospin Jastrow potential, 627 Jet, 693 JJ coupling: atomic, 356 nuclear, 540 J meson, 679 Josephson effect, 491 Kirchoff law, Klein-Gordon equation, 639 K meson, 644, 649 decay of, 658 Kronig Penney model, 457 Kurie plot, 569 Laguerre polynomials, associated, N-5 Lamb shift, 288 Lambda particle, 644 Lambda point, 402 Landé g- factor, 368 Landé interval rule, 359, 514 Lanthanide, 334 Laplacian operator, 235, 236, M-1 Larmor frequency, 270 Larmor precession, 270 Laser, 291, 392 Lattice tr an slation vector, Q-1 Laue diffraction pattern, 61 Legendre functions, associated, N-1 Legendre polynomials, N-1 Lenz law, 493 Lepton, 641 Lepton number conservation, 642 Leptoquark, 707 Level densities, of band, 463 Lifetime, 292, 558 Linearity of Schroedinger equation, 132, 166 Line spectrum, 97 formation of, 102, 348 Line width, 76 Liquid drop model, 526, 549 Liquid helium, 402 Local gauge symmetry, 688 Lorentz contraction, A-8 Lorentz transformation, A-11 (Ji LS coupling, 356 exclusion principle in, P-1 selection rules for, 364 Lyman series, 98 Magic numbers, 530, 561 Magnetic dipole moment: atomic, 365 nuclear, 512, 543 orbital, 267, 268 spin, 274 Magnetic field strength, 492 Magnetic induction, 492 Magnetic quantum number, 240 Magnetic resonance, nuclear, 392 Magnetic susceptibility, 493 Magnetization, 492 Majorana neutrino, 709 Many body effects: in nuclei, 545 in solids, 484 Many particle states, 595 Maser, 393 Mass deficiency, 523 Mass formula, 528 Mass number, 511 Mass spectrometry, 519 Mass unit, 520 Mass width, 652 Matrix element beta decay, 568 electric dipole, 290 electric quadrupole, 581 magnetic dipole, 581 nuclear, 569 pe rturbation, 771 and selection rules, 292 Matrix mechanics, 261 Matter waves, 56, 69 Maxwell dist ri bution, 3, 14, 377 Mean free path, 450 Meissner effect, 484 Meson, 650 See also specific types Meson theory, 634 Metallic bond, 445 Metallic solid, 445 Metastable state, 295, 393 Michelson-Morley experiment, A-4 Miller indices, Q-7 Mirror nuclei, 552, 601 Mobility, 451 Models an d theories, 509, 545 Moderator, 606 Molecular bond, 444 Molecular solid, 444 Momentum spectrum, 567 Moseley formula, 341 Miissbauer effect, 584 Multiple scattering, 89 Multiplet, 359 Multipolarity, 579 Muon, 641 Muonic atom, 106 Z m Muonic neutri no, 641 Natural line width, 76 Negative resistance, 477 Net potential: atomic, 320 nuclear, 531, 541 Neutral current process, 703 Neu tr ino, 566 electronic, 642 muonic, 641 production of, 667 tauonic, 642 Neutri no oscillations, 709 Neutron, 512 Neutron number, 526 Neutron-proton scattering, 622 Noble gas, 335 Normal Zeem an effect, 364 Normalization, 138, 149 in box, 182 n-type semiconductor, 468 Nuclear abundance, 526 Nuclear binding energy, 524 Nuclear charge density, 517 Nuclear electric quadrupole moment, 514, 546 Nuclear force, 511 coupling constant, 638 see also Nucleon force Nuclear interaction, 574 parity conse rv ation in, 595 see also Strong interaction Nuclear magnetic dipole moment, 512, 543 Nuclear magnetic resonance, 392 Nuclear magneton, 512 Nuclear mass, 519 Nuclear mass density, 518 Nuclear mass formula, 528 Nuclear matrix element, 569 Nuclear pairing interaction, 541 Nuclear parity, 542 Nuclear potential scattering, 591 Nuclear radius, 518 Nuclear reaction, 588 energy balance in, 521 Nuclear reactor, 602 Nuclear spin, 434, 512, 542 Nuclear spin-orbit interaction, 537 Nuclear spin quantum number, 435 Nuclear symmetry character, 434, 512 Nucleon, 512 Nucleon force, 618 See also Nuclear force Nucleon potential, 619 Nucleon resonances, 651 Nucleus, discovery of, 90 Numerical integration, G-7 Numerical solution of Schroedinger equation, G-1 Observed interactions, 653 Odd function, 142 Old quantum theory, c ri tique of, 118, 295 Omega meson, 652 Omega particle, 648 One-electron atom: eigenfunctions, 243 eigenvalues, 239 Schroedinger equation, 235 Operator angular momentum, 255, M-2 Laplacian, 235, M-1 linear momentum, 145 Operator equation, 145 Optical excitation, 348 Optically active electron, 349 Optical model, 592 Optical pumping, 396 Optical pyrometer, 3, 19 Optical spectra, 348 Orbital angular momentum, 254 and parity, 294 quantization of, 99 quantum mechanical conservation law for, 259 quantum numbers, 253 total, 355 Orbital g-factor, 269 Orbital magnetic dipole moment, 268 Orthogonality, 230, 307, 344, J-2 Ortho-molecule, 435 Pair annihilation, 43, 45 Pairing in covalent bonds, 421 in nuclei, 541 in superconductivity, 487 Pairing energy, 542 Pairing term, 527 Pair production, 43 cross section for, 49 Dirac theory of, 47 Paramagnetism, 493 Para-molecule, 435 Parent nucleus, 556 Parity, 220, 294, 576 conse rv ation in electromagnetic interaction, 576 conse rv ation in nuclear interaction, 595 intrinsic, 639 nonconservation in beta decay, 576 nuclear, 542 operation, 294 and orbital angular momentum, 294 an d selection rules, 295, 572, 580 Pa rt ial b an d, 499 Pa rt ial derivative, 127 Particle in a box, 215 Particle-wave duality, see Wave-particle duality Pa rt on, 667 Paschen-Bach effect, 370 Paschen series, 98 Pauli principle, see Exclusion principle Penetration of classically excluded region, 189 Penetration distance, 190 Periodic table, 330, 331 Permanent magnetism, 501 Pe rturbation theory: time dependent, K-1 time independent, J-1 Pfund series, 98 Phase integral, 111 Phase space, 111, 409 Phi meson, 652 Phipps-Taylor experiment, 273 Phonon, 399, 484 Quantum electrodynamics, 288, 291, 295, 635, 639, 685, 690 Quantum number, 20, 100, 238 See also specific types and superconductivity, 487 Phonon wing, 585 Quantum statistics, 377 Phosphorescence, 295 Photoconductivity, 467 Photoelectric effect, 27 cross section for, 49 Einstein theory of, 29 Photoelectron, 28 Photon, 40, 650, 653 momentum of, 35 rest mass of, 35 Photon gas, 34, 398 Pi meson, see Pion Pickering series, 123 Pion, 634, 653 Pion field, 634 Pion resonances, 651 Planck blackbody spectrum, 17 theory of, 13, 398 Planck const ant, 16, 31 Planck energy quantization, 20, 410 and Schroedinger theory, 222 and Wilson-Sommerfeld rules, 111 Planck postulate, 20 Plasma, 609 p-n junction, 472 Polar molecule, 418 Population inversion, 396 Positron, 43, 464 Positron emission, 564 Positronium, 45, 106, 466 Pound-Rebka experiment, 588 Power series technique, I-3 Poynting vector, 63, B-2 Preons, 710 Primitive unit cell, Q-2 Principal quantum number, 115, 240, 535 Probability density, 135, 244 average, 252 directional, 249 radial, 244 Probability flux, 196 Product particle, 521 Prompt fission neutron, 605 Proper length, A-8 A-8 Propetim, Protn,51 Proton-proton cycle, 609 Psi meson, 679 p-type semiconductor, 469 Quantization: of action, 111 of energy, see Energy quantization of magnetic flux, 491 of orbital angular momentum, 99, 254 space, 273 of spin angular momentum, 274 Quantum chromodynamics, 691 Quantum Mate, 20,166 Quark, 673, 676, 678 mass of, 682 Quark quantum number, 682 Q-value, 522, 589 Rad, unit, 616 Radial node quantum number, 534 Radial probability density, 244 Radiancy, Radiation: by accelerated charge, B-1 by atoms and Bohr model, 99 by atoms and Schroedinger theory, 167 intensity, 63 Radioactive series, 560 Radioactivity, 555 Radius: atomic, 86, 327 Bohr, 100, 246 nuclear, 518 Raman effect, 432 Ramsauer effect, 202, 229, 592 Range of interaction: beta, 574, 653 electromagnetic, 636, 653 gravitational, 574, 653 nuclear, 635, 653 Rare earth, 334 Rayleigh-Jeans blackbody theory, Rayleigh-Jeans spectrum, 12 Rayleigh scattering, 38, 49, 55, 432 Reaction, nuclear, 588 Reactor fusion, 607 nuclear, 602 Real part, F-1 Reciprocal wavelength, 70 Reciprocity property, 197 Recombination current, 473 Rectifiers, 472 Recursion relation, I-4 Reduced mass, 105, 233 Reflection coefficient, 188, 196 Regeneration, 660 Reines-Cowan experiment, 575 Relativistic energy, A-15 Relativistic mass, 523, A-14 Relativity theory, A-1 and electron spin, 277 and hydrogen atom, 116, 286 Renormalization, 700 Repulsive core, 627, 629 Residual Coulomb interaction, 353 Residual nucleus, 521 Resistance, 450, 464 negative, 477 Resistivity, 450 Resonances, pion-nucleon, 651 Z v m 00 X W Z Resonant absorption, 584 Rest mass, A-14 Rest mass energy, A-16 Rho meson, 652 Rigid rotator, 264, 299, 423, 599 Rotational quantum number, 424 Rotational spectra: molecular, 423 nuclear, 599 selection rules, 424 Ruby laser, 396 Russell-Saunders coupling, 356 Ruth erford model, 90 Rutherford scattering, 90, E-1 cross-section for, 95, 591 Rydberg constant for finite nuclear mass, 105 for hydrogen, 97 for infinite nuclear mass, 102 Saturation: in molecular binding, 422 of nuclear forces, 524, 618, 629 Scattering, nuclear, 88, 593 Scattering probability flux, L-4 Schmidt line, 543 Schottky specific heat, 413, 506 Schroedinger equation, 132 an d de Broglie postulate, 129 an d differential operators, 145 and Dirac theory, 132 and Newton law, 184 plausibility argument for, 128 Screened Coulomb potential, L-7 Selection rules: for alkali atoms, 351 for beta decay, 572 an d correspondence principle, 117 for gamma decay, 580 for LS coupling, 364 for matrix elements, 292 for one-electron atoms, 288 x-ray, 340 Self-conjugate, 641 Self-consistency, 320 Semiconductor, 450, 467 Semiempirical mass formula, 528 Separation constant, 152 Separation of va ri ables, 151 in one-electron atom Schroedinger equation, 235 Serber potential, 624 Series limit, 97 Series solution of Schroedinger equation, I-1 Shell, 246, 325 Shell model, 534, 549 excited states of, 599 predictions of, 540 Sigma particle, 648 Simple harmonic oscillator classical limit of, 117, 136, 165 eigenfunctions of, 223 eigenvalues of, 222 energy levels in old quantum theory, 20 ground state probability density, 136 ground state wave function, 133 phase diagram, 111 potential for, 221 series solution of, I-1 Simultaneity, A-5 Single particle state, 592 Singlet state, 312 Single-valuedness: of eigenfunction and derivative, 155 of one-electron atom eigenfunction, 237 Size resonance, 202, 592 Slater determinant, 309 Solar cell, 27 Solar constant, 23 Solid an gle, 95 Sommerfeld model, 114 and hydrogen energy levels, 286 Space quantization, 273 Specific heat, 388 Debye, 390 Einstein, 388 Electronic, 406 Shottky, 413 Spectral line, 97, 102 Spectral radiancy, Spectroscopic notation, 331, 339, 358 Spectroscopy, 97 Spherical polar coordinates, 235, M-1 Spin: electron, 272, 274 nuclear, 434, 512, 542 total, 355 Spin dependence of nucleon potential, 621 Spin eigenfunction, 311 Spin g- factor, 274 Spin magnetic dipole moment, 274 Spin-orbit interaction, 278 in alkali atoms, 350, 372 general formula for, 285 in multielectron atoms, 353 in nuclear potential, 537 in nucleon potential, 629 an d Thomas precession, O-1 Spin qu antum number electron, 274 nuclear, 435, 512, 542 total, 358 Spin resonance, electron, 369 Spontaneous emission, 291, 393 Spontaneous fission, 560, 603 Spontaneous symmetry breaking, 700 Square well potential, 209 analytical solution of, H-1 numerical solution of, G-1 Standing waves, 8, 113 Stefan-Boltzmann constant, Stefan law, and Planck spectrum, 19 Stellar formation, 609 Step potential (E < V0 ), 184 (E > V0 ), 193 Steradian, 597 Ste rn-Gerlach experiment, 272 Stimulated absorption, 393 Stimulated emission, 291, 393 Stopping potential, 28 Strangeness, 643, 644 Strange particles, 643 Strong coupling constant, 699 Strong interaction, 641, 653, 655 See also Nuclear interaction Subshell, 252, 329 properties when filled, 252, 363 Superconducting state, 484 Superconductor, 484 type II, 491 Superfluid, 402 Supergravity, 710 Superheavy elements, 561 Supe rnova, 611 Superposition principle, 64 Supersymmetry theory, 710 Surface term, 527 Susceptibility, 493 paramagnetic, 495 SU (2) theory, 673 SU (3) theory, 674, 678 Symmetric eigenfunction, 305 Symmetry character, 310 nuclear, 435, 512 Target nucleus, 521 Tau particle, 647 Tauonic neut rino, 642 Tauons, 642 Taylor experiment, 77 Thermal current, 473 Thermal equilibrium, 381, C-1 Thermal radiation, See also Blackbody radiation Thermionic emission, 407 Theta particle, 647 Thomas frequency, O-3 Thomas precession, O-1 Thomson experiment, 58 Thomson model, 86 Time, flow of, 660 Time dilation, A-8 Time-independent Schroedinger equation, 150 and classical wave equation, 203 and energy quantization, 156 plausibility argument for, 154 Time reversal, 657 Total angular momentum, 281, 355 Total internal reflection, 203 Total magnetic dipole moment, 365 Total orbital angular momentum, 355 Total radial probability density, 323 Total relativistic energy, A-16 Total spin angular momentum, 312, 355 Transistor, 474 Tran sition group, 336 Tr an sition probability, K-4 Tran sition rates: for alpha decay, 207 for beta decay, 570 for electric dipole radiation, 290 for gamma decay, 579 and selection rules, 288, 289 Transmission coefficient, 196 Trian gle anomaly, 705 Triplet state, 312 T ri tium, 571 Tunnel diode, 209, 475 Tunneling, 199, 201, 558, 603 Type II superconductor, 491 Ultraviolet catastrophe, 13 Uncertainties, 150 Uncertainty principle, 65 consequences of, 77 and de Broglie postulate, 72 and infinite square well, 150 interpretation of, 66 an d stability of atom, 248 an d statistical nature of qu antum theory, 139 verification of, 586 and wave-particle duality, 191 and zero- point energy, 217 Unitary group, 701 Unitary symmetry, 673 Unit cell, 448, Q-1 primitive, Q-2 Universal °K blackbody radiation, 20, 609 Vacuum polarization, 699 Valence, 336 Valence band, 450 Van Allen belts, 42 Van der Waals attraction, 444 Vector meson, 652 Vector model, 258, 283 Vector potential, 689 Vibrational qu an tum number, 426 Vibrational spectra, 427 molecular, 426 nuclear, 600 Vibration-rotation spectra, 426 Virial theorem, 263 Virtual particle, 634 Volume term, 527 W± particles, 702 Wave function, 64, 134, 166 interpretation of, 64, 134 and probability density, 135 Wave group, 70 Wave number, 129 Wave velocity, 72 Wave-particle duality, 62 an d matter, 56 and radiation, 40 Weak interaction, 641, 647, 653 See also Beta decay Weak isospin, 702 Weak mixing an gle, 702 Width of energy levels, 583 Wien displacement law, 4, and Planck spectrum, 19 Wilson-Sommerfeld quantization rules, 111 Work function, 30, 408 Wu experiment, 575 X Q Z Yukawa potential, 638 Yukawa theory, 634 Xi particle, 648 X-ray, 32, 40 X-ray continuum spectrum, 41 X-ray line spectrum, 337 X-ray production, 40, 42, 337 X-ray selection rules, 340 X-ray tube, 41 Z° particle, 702 Zeeman effect, 274, 364 Zero point energy, 217, 429 of electromagnetic field, 291 and stability of atom, 248 Zero potential, 178 Zweig forbidden, 679 Yang-Mills theory, 690 Date Due SIUKA-S #P R777 Return this book on or before the last date stamped below $ Useful Constants and Conversion Factors Quoted to a useful number of significant figures Avogadro's number Coulomb's law constant c = 2.998 x 10 m/sec e = 1.602 x 10 -19 coul h = 6.626 x 10 -34 joule-sec h = h /2n = 1.055 x 10 -34 joule-sec = 0.6 82 x 10 -15 eV-sec k =1.381 x 10 -23 joule / °K = 8.617 x 10 -5 eV/ °K No = 6.023 x 1023/mole /47cE0 = 8.988 x 109 nt - m2 /coul2 Electron rest mass Proton rest mass Neutron rest mass Atomic mass unit (C 12 - 12) me = 9.109 x 10 -31 kg 0.5110 MeV/c mp = 1.672 x 10 -27 kg =938.MeV/c mn = 1.675 x 10 -27 kg 2=93.6MeV/c 931.5MeV/c u = 1.661 x 10 -27 kg= Bohr magneton Nuclear magneton Bohr radius Bohr energy µ b = eh/2m, = 9.27 x 10 -24 amp-m2 (or joule/tesla) Speed of light in vacuum Electron charge magnitude Planck's constant Boltzmann's constant = eh /2m p = 5.05 x 10 -27 amp-m (or joule/tesla) ao = 47rEOh2/mee2 = 5.29 x 10 -11 m = 0.529 A -18 E1 = — mee4/( 47cE0) 22h2 = —2.17 x 10 joule = —13.6 eV Electron Compton wavelength Ac = h/mec = 2.43 x 10 -12 m = 0.0243 A Fine-structure constant a = e2 /47cEOhc = 7.30 x 10 -3 ^ 1/137 k300 °K = 0.0258 eV ^ 1/40 eV kT at room temperature eV = 1.602 x 10 -19 joule 1A =10 -10 m 1F=10 -15 m joule = 6.242 x 10 18 eV barn (bn) = 10 -28 m2 ... explanations of the properties of atoms, molecules, solids, nuclei, and particles The „ QUANTUM PHYSICS of Atoms, Molecules, Solids, Nuclei, and Particles Second Edition ROBERT EISBERG University of California,... John Wiley & Sons Library of Congress Cataloging in Publication Data: Eisberg, Robert Martin Quantum physics of atoms, molecules, solids, nuclei, and particles Includes index Quantum theory I Resnick, ... York Robert Eisberg Robert Resnick PREFACE TO THE FIRST EDITION The basic purpose of this book is to present clear and valid treatments of the properties of almost all of the important quantum