An Introduction to Quantum Physics. The M.I.T. Introductory Physics Series

685 Pages·1978·10.29 MB·English

by  Edwin French A. P.

An. Introduction-
to A antu"L-
Physics
A. P. FRENCH
EDWIN F. TAYLOR
8i
THE 'M.i1.T.
INTRODUCTORY
1
PHYSICS SERIES
An
Introduction
to
Quantum
Physics
A. P. French
I'K()I I ',NOR ()f Till'I( ti IIII ti11ti'A( HUtiI I IS INSIIIUII ()F II( IIN()I ()(,Y
Edwin F. Taylor
SF NIOR RFSFAR( H S( If N I IS! I HF MASSA( HUSF T IS INS! I I U I F OF I f ( HN()I ()(6Y
An
Introduction
to
Quantum
Physics
THE M.I.T. INTRODUCTORY PHYSICS SERIES
W W NORTON & COMPANY INC NEW YORK
W W Norton & Company Inc 500 Fifth Avenue New York N Y 10110
(o 1978 hN Ilic 11/1(1SS(i( /iit sc'It S /iiSittitIc of I c( /lii()/() t'vv
Library of Congress Cataloging in Publication Data
French. Anthony Philip.
An Introduction to Quantum physics
(The M.I.T. introductory physics series)
Bibliography p.
Includes index.
I Quantum theory. I. Taylor, Edwin F.. co-
author 11. Title. III. Series: Massachusetts Institute of Technology
Education Research Center. M.I.T. introductory physics series.
QC 174 12.1`73 530.1'2 78-4853
ISBN 0-393-09106-0
Pi iiitc'(l iii ili(' Ciiite(l .S tatc Bill('/ ( (I
A/f Rig/its R('Sci I (l
Contents
PREFACE X1
LEARNING AIDS FOR QUANTUM PHYSICS VV
1 Simple models of the atom
1-1 Introduction 1
1-2 The classical atom 4
1-3 The electrical structure of matter 5
1-4 The Thomson atom 11
1-5 Line spectra 14
1-6 Photons 17
1-7 The Rutherford-Bohr atom 24
1-8 Further predictions of the Bohr model 29
1-9 Direct evidence of discrete energy levels 30
1-10 X-ray spectra 33
1-11 A note on x-ray spectroscopy 39
1-12 Concluding remarks 43
EXERCISES 45
2 The wave properties of particles 55
2-1 De Broglie's hypothesis 55
2-2 De Broglie vaves and particle velocities 58
2-3 Calculated magnitudes of De Broglie wavelengths 6-
2-4 The Davisson-Germer experiments 64
2-5 More about the Davisson-Germer experiments 68
2-6 Further manifestations of the wave propertless o/
electrons 72
2-7 Wave properties of neutral atoms and molecules 78
2-8 Wave properties of'nuclear particles 82
V
2--9 1 he fneanini' of the 1t 'al'e-parti('le (111ality' 85
2 /0 1'lic' c'oc'.CI.S1('nc c of w'al'e (lilt/ particle propertie.S 87
1 A first discus %iou of c/ii(iiltilm (1111plitiides 93
1 \1 R( ItiI s 95
Wave-particle duality and bound states 1 05
3-1 Preliininarl' reinarh.S 105
3-2 The approach to a particle-u'a1'e ('l/Nation 107
3-3 The Schrodinger equation /09
3-4 Stationarv .States 112
3-5 Particle in a box 113
3-6 Unique energy without unique moilieliti(ln 117
3-7 Interpretation o t the quantum ainplitude S for bound
.State.% 119
3-8 Particles in ilonrigid boxes 123
3-9 Square well of ,finite depth 12 7
3- 10 of the t'al'e ,function 129
3-11 Qualitative plots of hound-,State t'al'l',f illiction.S 131
I XE.R( ISLS 145
4 Solutions of Schrodinger's equation in one dimension 155
4-1 Introduction 155
4-2 The square 1t'ell 156
4-3 The harmonic oscillator 162
4-4 Vibrational energies of diatomic molecules 170
4-5 Computer solution,s of the Schrodinger equation 174
EXERCISES 182
5 Further applications of Schrodinger's equation 193
5-1 Introduction 193
5-2 The three-dimensional Schrodinger equation 193
5-3 Eigenfunctions and eigenvalue,S 195
5-4 Particle in a three-dimensional box 196
5-5 Spherically syminetric solution.s for hydro en-like
.S 1'.S tem.S 199
5-6 Normalization and probability den.Sitie.S 208
5-7 Expectation values 211
5-8 Computer solutions for spherically .s minetric hydrogen
functions 216
EXERCISES 219
6 Photons and quantum states 231
6-1 Introduction 231
6-2 States of linear polarization 233
6-3 Linearly polarized photons 237
6-4 Probability and the behavior of polarized photons 241
vi Contents
6-5 States of circular polarization 243
6-6 Orthogonality and completeness 246
6-7 Quantum states 250
6-8 Statistical and classical properties of light 253
6-9 Concluding remarks 254
APPENDIX: POLARIZED LIGHT AND ITS PRODUCTION 256
6A-1 The production of linearly polarized light 256
6A-2 The production of circularly polarized light 261
Suggested experiments with linearly polarized light 266
EXERCISES 270
7 Quantum amplitudes and state vectors 279
7-1 Introduction 279
7-2 The analyzer loop 280
7-3 Paradox of the recombined beams 283
7-4 Interference effect in general 285
7-5 Formalism of projection amplitudes 288
7-6 Properties of projection amplitudes 290
7-7 Projection amplitudes for states of circular
polarization 294
7-8 The state vector 298
7-9 The state vector and the Schrodinger w'ave function for
bound states 304
EXERCISES 306
8 The time dependence of quantum states 315
8-1 Introduction 315
8-2 Superposition of states 316
8-3 An example of motion in a box 317
8-4 Packet states in a square-well potential 321
8-5 The position-momentum uncertainty relation 327
8-6 The uncertainty principle and ground-state energies 330
8-7 Free-particle packet states 331
8-8 Packet states for moving particles 336
8-9 Examples of moving packet states 338
8-10 The energy-time uncertainty relation 343
8-11 Examples of the energy-time uncertainty relation 345
8-12 The shape and width of energy levels 351
EXERCISES 354
9 Particle scattering and barrier penetration 367
9-1 Scattering processes in terms of wave packets 367
9-2 Time-independent approach to scattering
phenomena 369
9-3 Probability density and probability current 374
9-4 Scattering by a one-dimensional well 379
9-5 Barrier penetration: tunneling 383
vii Contents
9-6 Probability eutrent and barrier penetration proble,ns 389
9-7 An appioximatiori for barrier penetration
c'(ilc'iilatic)n S 392
9-8 Field emission 0/ . electroits 395
9-9 .S'plie, a all v svFninetrie probability currents 399
9-10 Quantitative theory of alpha decay 403
9-11 Scattering of vavve 408
I X1 R('ISI S 414
10 Angular momentum 425
10-1 Introduction 425
10-2 Stern-G erlacli experiment: theory 428
10-3 Stern-Gerlach experiment: descriptive 432
10-4 Magnitudes of atomic dipole moments 438
10-5 Orbital angular momentum operators 442
10-6 Eigenvalues of Lz 445
10-7 Simultaneous eigenvalues 449
10-8 Quantum states of f a two-dimensional harmonic
oscillator 454
EXERCISES 462
11 Angular momentum of atomic systems 473
11-1 Introduction 473
11-2 Total orbital angular momentum in central fields 473
11-3 Rotational states of molecules 487
11-4 Spin angular momentum 500
11-5 Spin orbit coupling energy 502
11-6 Formalism for total angular momentum 505
APPENDIX: THE SCHRODINGER EQUATION IN SPHERICAL
COORDINATES 506
EXERCISES 509
12 Quantum states of three-dimensional systems 519
12-1 Introduction 519
12-2 The Coulomb model 519
12-3 General features of the radial wave functions for
hydrogen 523
12-4 Exact radial wave functions for hydrogen 528
12-5 Complete Coulomb wave functions 531
12-6 Classification of energy eigenstates in hydrogen 537
12-7 Spectroscopic notation 539
12-8 Fine structure of hydrogen energy levels 540
12-9 Isotopic fine structure: heavy hydrogen 544
12-10 Other hydrogen-like systems 546
EXERCISES 550
Viii Contents
13 Identical particles and atomic structure 557
13-1 Introduction 557
13-2 Schrvdinger's equation for two noninteracting
particles 558
13-3 The consequences of identity 561
13-4 Spin states for two particles 564
13-5 Exchange symmetry and the Pauli principle 566
13-6 When does symmetry or antisymmetry matter? 569
13-7 Measurability of the symmetry character 571
13-8 States of the helium atom 575
13-9 Many-electron atoms 587
13-10 General structure of a massive atom 595
EXERCISES 598
14 Radiation by atoms 605
14-1 Introduction 605
14-2 The classical Hertzian dipole 605
14-3 Radiation from an arbitrary charge distribution 608
14-4 Radiating dipoles according to wave mechanics 612
14-5 Radiation rates and atomic lifetimes 615
14-6 Selection rules and radiation patterns 617
14-7 Systematics of line spectra 626
14-8 Angular momentum of f photons 628
14-9 Magnetic dipole radiation and galactic hydrogen 631
14-10 Concluding remarks 637
EXERCISES 638
BIBLIOGRAPHY
ANSWERS TO EXERCISES
SEI ECTED PHYSICAL CONSTANTS AND CONVERSION I-AC IORS
INDEX
ix Contents