An introduction to quantum physics:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton
CRC Press
2017
|
| Edition: | First issued in hardback |
| Series: | M.I.T. introductory physics series
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Physical Description: | xviii, 670 Seiten Illustrationen |
| ISBN: | 9781138464667 9780748740789 |
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| adam_text | Contents
PREFACE Xi A
LEARNING AIDS FOR QUANTUM PHYSICS XV
Simple models of the atom 1
l-l Introduction J
1-2 The classical atom 4
1-3 The electrical structure of matter 5
1-4 The Thomson atom II
1-5 Line spectra 14
1-6 Photons 17
1-7 The Rutherford-Bohr atom 24
IS Further predictions of the Bohr model 29
1-9 Direct evidence of discrete energy levels 30
1-10 X-ray spectra 33
¡-11 A note on x-ray spectroscopy 39
1-12 Concluding remarks 43
EXERCISES 45
The wave properties of particles 55
2- De Broglie s hypothesis 55
2-2 De Broglie waves and particle velocities 58
2-3 Calculated magnitudes of De Broglie wavelengths 62
2-4 The Davisson-Germer experiments 64
2-5 More about the Davisson-G ermer experiments 68
2-6 Further manifestations of the wave properties of
electrons 72
2-7 Wave properties of neutral atoms and molecules 78
2-8 Wave properties of nuclear particles 82
V
2-9 The meaning of the wave-particle duality 85
2- ¡0 The coexistence of wave and particle properties 87
2- il A first discussion of quantum amplitudes 93
exercises 95
3 Wave-particle duality and bound states
105
3-1 Preliminary remarks 105
3-2 The approach to a particle-wave equation 107
3-3 The Schrodinger equation ¡09
3-4 Stationary states ¡12
3-5 Particle in a one-dimensional box ¡13
3-6 Unique energy without unique momentum J ¡7
3-7 Interpretation of the quantum amplitudes for bound
states I ¡9
3-8 Particles in nonrig id boxes 123
3-9 Square well of finite depth ¡27
3-10 Normalization of the wave function 129
3-11 Qualitative plots of bound-state wave functions I3i
exercises ¡45
4 Solutions of Schrôdinger’s equation in one dimension 155
4-¡ introduction ¡55
4-2 The square well ¡56
4-3 The harmonic oscillator ¡62
4-4 Vibrational energies of diatomic molecules ¡70
4-5 Computer solutions of the Schrodinger equation ¡74
exercises ¡82
5 Further applications of Schrddinger’s equation 193
5-¡ Introduction ¡93
5-2 The three-dimensional Schrodinger equation ¡93
5-3 Eigenfunctions and eigenvalues ¡95
5-4 Particle in a three-dimensional box ¡96
5-5 Spherically symmetric solutions for hydrogen-like
systems ¡99
5-6 Normalization and probability densities 208
5-7 Expectation values 2H
5-8 Computer solutions for spherically symmetric hydrogen
wave functions 2/6
EXERCISES 2/9
6 Photons and quantum states
6-1 Introduction 23 i
6-2 States of linear polarization 233
6-3 Linearly polarized photons 237
6-4 Probability and the behavior of polarized photons
231
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
6A-1 The production of linearly polarized light 256
6A-2 The production of circularly polarized light 261
Suggested experiments with linearly polarized light
exercises 270
7 Quantum amplitudes and state vectors
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 wave 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
256
266
279
VII
Contents
9-6 Probability current and barrier penetration problems 389
9-7 An approximation for barrier penetration
calculations 392
9-8 Field emission of electrons 395
9-9 Spherically symmetric probability currents 399
9-10 Quantitative theory of alpha decay 403
9- 11 Scattering of wave packets 408
exercises 414
10 Angular momentum
10- 1 Introduction 425
10-2 Stern-Gerlach experiment: theory 428
10-3 Stern-G erlach 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 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 Schrddinger*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
¡4-1 Introduction 605
14-2 The classical Hertzian dipole 605
14-3 Radiation from an arbitrary charge distribution 608
¡4-4 Radiating dipoles according to wave mechanics 612
¡4-5 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 photons 628
14-9 Magnetic dipole radiation and galactic hydrogen 631
14-10 Concluding remarks 637
exercises 638
BIBLIOGRAPHY
ANSWERS TO EXERCISES
SELECTED PHYSICAL CONSTANTS AND CONVERSION FACTORS
INDEX
ix
Contents
An introduction to Quantum Physics
A, P. French E. F. Taylor
M.I.T.
Introductory
Physics
Series
The M.l.T. Introductory Physics Series is
the result of a program of careful study,
planning and development that began in
1960. The Education Research Center at
the Massachusetts Institute of Technology
(formerly the Science Teaching Center) was
established to study the process of
instruction, aids thereto and the learning
process itself, with special reference to
science teaching at the university level.
Generous support from the National Science
Foundation and from the Kettering, Shell,
Victoria. W. T. Grant and Bing Foundations
provided the means for assembling and
maintaining an experienced staff to co-
operate with members of the Institute s
Physics Department in the examination,
improvement and development of physics
curriculum materials for students planning
careers in the sciences.
This book covers the fundamentals of
quantum physics through the full Coulomb
theory of the hydrogen atom, a semi-
quantitative analysis of the helium atom,
and a qualitative description of the build-
up of the periodic table, ending with a brief
discussion of radiation by atoms. The
emphasis throughout is on the experimental
and theoretical underpinnings of quantum
mechanics with examples from various
areas of physics selected to illuminate how
the theory works in practice. The authors
have chosen to concentrate on a
development of the Schrôdinger method,
but have introduced the matrix notation
and indicated some relations between the
two descriptions.
After careful analysis of objectives and the
problems involved, preliminary versions of
textbooks were prepared, tested through
classroom use at M.l.T. and other
institutions, re-evaluated, rewritten and
tried again. Only then were the final
manuscripts undertaken. In general the
books in the Series will be brief. Most may
be covered in a single term or less. Their
brevity and structure (as well as their
reasonable price) will make it possible for
teachers to select topics and organize
courses according to individual needs and
preferences.
The complete series will cover the
appropriate constituents for a wide
variety of introductory one- and two-
year courses at the university level.
CRC Press
Taylor Francis Croup
an informa business
www,crcpress.com
ISBN 978-1-138-46466-7
|
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| title_short | An introduction to quantum physics |
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| topic_facet | Quantentheorie Quantenphysik Quantenmechanik Einführung Lehrbuch |
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| work_keys_str_mv | AT frenchap anintroductiontoquantumphysics AT tayloredwinf anintroductiontoquantumphysics |