Quantum Principles and Particles

by Wilcox; Walter

• ISBN13: 9781439835258
• ISBN10: 143983525X
• Format: Nonspecific Binding
• Copyright: 2012-04-06
• Publisher: CRC Press

Summary

Inspired by the work of Nobel laureate Julian Schwinger, this book provides a clear, extensively illustrated introduction to quantum mechanics. It uses a combined approach of wave mechanics and spin analysis to explain the concepts of particle physics. The author#xE2;#xAC;"s pedagogical approach uses special process diagrams as tools for visualizing the states and operators as well as for illustrating ways to compute amplitudes for quantum mechanical processes. Problem sets build from the text and reinforce key principles. The first part of the book covers all the essential principles for the development of quantum mechanics. The second half focuses on quantum particles.

Table of Contents

Preface	p. xiii
Author	p. xvii
Quantum Principles
Perspective and Principles	p. 3
Prelude to Quantum Mechanics	p. 3
Stern-Gerlach Experiment	p. 7
Idealized Stern-Gerlach Results	p. 12
Classical Model Attempts	p. 15
Wave Functions for Two Physical-Outcome Case	p. 21
Process Diagrams, Operators, and Completeness	p. 25
Further Properties of Operators	p. 28
Operator Reformulation	p. 37
Operator Rotation	p. 39
Bra-Ket Notation/Basis States	p. 46
Transition Amplitudes	p. 47
Three-Magnet Setup Example-Coherence	p. 50
Hermitian Conjugation	p. 53
Unitary Operators	p. 56
A Very Special Operator	p. 57
Matrix Representations	p. 58
Matrix Wave Function Recovery	p. 62
Expectation Values	p. 64
Wrap Up	p. 65
Problems	p. 66
Particle Motion in One Dimension	p. 77
Photoelectric Effect	p. 77
Compton Effect	p. 79
Uncertainty Relation for Photons	p. 83
Stability of Ground States	p. 85
Bohr Model	p. 86
Fourier Transform and Uncertainty Relations	p. 88
Schrödinger Equation	p. 90
Schrödinger Equation Example	p. 94
Dirac Delta Functions	p. 97
Wave Functions and Probability	p. 99
Probability Current	p. 102
Time Separable Solutions	p. 103
Completeness for Particle States	p. 104
Particle Operator Properties	p. 107
Operator Rules	p. 110
Time Evolution and Expectation Values	p. 112
Wrap-Up of Chapter 2	p. 114
Problems	p. 115
Some One-Dimensional Solutions to the Schrödinger Equation	p. 121
Introduction	p. 121
The Infinite Square Well: Differential Solution	p. 123
The Infinite Square Well: Operator Solution	p. 129
The Finite Potential Barrier Step Potential	p. 134
The Harmonic Oscillator	p. 140
The Attractive Kronig-Penny Model	p. 149
Bound State and Scattering Solutions	p. 155
Problems	p. 156
Hilbert Space and Unitary Transformations	p. 161
Introduction and Notation	p. 161
Inner and Outer Operator Products	p. 163
Operator-Matrix Relationship	p. 165
Hermitian Operators and Eigenkets	p. 166
Gram-Schmidt Orthogonalization Process	p. 168
Compatible Operators	p. 170
Uncertainty Relations and Incompatible Operators	p. 172
Simultaneously Measureable Operators	p. 175
Unitary Transformations and Change of Basis	p. 176
Coordinate Displacements and Unitary Transformations	p. 180
Schrödinger and Heisenburg Pictures of Time Evolution	p. 181
Free Gaussian Wave Packet in the Heisenberg Picture	p. 184
Potentials and the Ehrenfest Theorem	p. 185
Problems	p. 186
Three Static Approximation Methods	p. 191
Introduction	p. 191
Time-Independent Perturbation Theory	p. 192
Examples of Time-Independent Perturbation Theory	p. 195
Aspects of Degenerate Perturbation Theory	p. 198
WKB Semiclassical Approximation	p. 198
Use of the WKB Approximation in Barrier Penetration	p. 202
Use of the WKB Approximation in Bound States	p. 204
Variational Methods	p. 207
Problems	p. 212
Generalization to Three Dimensions	p. 217
Cartesian Basis States and Wave Functions in Three Dimensions	p. 217
Position/Momentum Eigenket Generation	p. 219
Example: Three-Dimensional Infinite Square Well	p. 222
Spherical Basis States	p. 224
Orbital Angular Momentum Operator	p. 225
Effect of Angular Momentum on Basis States	p. 226
Energy Eigenvalue Equation and Angular Momentum	p. 230
Complete Set of Observables for the Radial Schrödinger Equation	p. 232
Specification of Angular Momentum Eigenstates	p. 234
Angular Momentum Eigenvectors and Spherical Harmonics	p. 240
Completeness and Other Properties of Spherical Harmonics	p. 245
Radial Eigenfunctions	p. 248
Problems	p. 248
Quantum Particles
The Three-Dimensional Radial Equation	p. 255
Recap of the Situation	p. 255
The Free Particle	p. 257
The Infinite Spherical Well Potential	p. 264
The "Deuteron"	p. 267
The Coulomb Potential: Initial Considerations	p. 280
The Coulomb Potential: 2-D Harmonic Oscillator Comparison	p. 283
The Confined Coulombic Model	p. 299
Problems	p. 307
Addition of Angular Momenta	p. 317
General Angular-Momentum Eigenstate Properties	p. 317
Combining Angular Momenta for Two Systems	p. 319
Explicit Example of Adding Two Spin 1/2 Systems	p. 324
Explicit Example of Adding Orbital Angular Momentum and Spin 1/2	p. 326
Hydrogen Atom and the Choice of Basis States	p. 331
Hydrogen Atom and Perturbative Energy Shifts	p. 334
Problems	p. 338
Spin and Statistics	p. 343
The Connection between Spin and Statistics	p. 343
Building Wave Functions with Identical Particles	p. 344
Particle Occupation Basis	p. 347
More on Fermi-Dirac Statistics	p. 352
Interaction Operator and Feynman Diagrams	p. 354
Implications of Detailed Balance	p. 357
Cubical Enclosures and Particle States	p. 362
Maxwell-Boltzman Statistics	p. 364
Bose-Einstein Statistics	p. 366
Fermi-Dirac Statistics	p. 370
The Hartree-Fock Equations	p. 375
Problems	p. 379
Quantum Particle Scattering	p. 387
Introduction	p. 387
The One-Dimensional Integral Schrödinger Equation	p. 388
Reflection and Transmission Amplitudes	p. 392
One-Dimensional Delta-Function Scattering	p. 393
Step-Function Potential Scattering	p. 396
The Born Series	p. 402
The Three-Dimensional Integral Schrödinger Equation	p. 404
The Helmholtz Equation and Plane Waves	p. 407
Cross Sections and the Scattering Amplitude	p. 411
Scattering Phase Shifts	p. 412
Finite-Range Potential Scattering	p. 416
The Three-Dimensional Born Series	p. 421
Identical Particle Scattering	p. 426
Proton-Proton Scattering	p. 430
Problems	p. 434
Connecting to the Standard Model	p. 443
Discrete Symmetries	p. 443
Parity	p. 444
Time Reversal	p. 448
Charge Conjugation	p. 453
Particle Primer	p. 454
Particle Interactions	p. 460
Quantum Electrodynamics	p. 461
Quantum Chromodynamics	p. 463
Weak Interactions	p. 468
Supersymmetry	p. 472
Superstrings	p. 474
Postlude	p. 477
Helpful Books on Particle and String Physics	p. 477
Problems	p. 478
Notation Comments and Comparisons	p. 485
Lattice Models	p. 487
2-D Harmonic Oscillator Wave Function Normalization	p. 493
Allowed Standard Model Interactions	p. 495
The Ising Model and More	p. 497
Weak Flavor Mixing	p. 509
Index	p. 523
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