Quantum Principles and Particles

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  • Edition: 1st
  • Format: Nonspecific Binding
  • Copyright: 2012-04-06
  • Publisher: CRC Press

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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

Prefacep. xiii
Authorp. xvii
Quantum Principles
Perspective and Principlesp. 3
Prelude to Quantum Mechanicsp. 3
Stern-Gerlach Experimentp. 7
Idealized Stern-Gerlach Resultsp. 12
Classical Model Attemptsp. 15
Wave Functions for Two Physical-Outcome Casep. 21
Process Diagrams, Operators, and Completenessp. 25
Further Properties of Operatorsp. 28
Operator Reformulationp. 37
Operator Rotationp. 39
Bra-Ket Notation/Basis Statesp. 46
Transition Amplitudesp. 47
Three-Magnet Setup Example-Coherencep. 50
Hermitian Conjugationp. 53
Unitary Operatorsp. 56
A Very Special Operatorp. 57
Matrix Representationsp. 58
Matrix Wave Function Recoveryp. 62
Expectation Valuesp. 64
Wrap Upp. 65
Problemsp. 66
Particle Motion in One Dimensionp. 77
Photoelectric Effectp. 77
Compton Effectp. 79
Uncertainty Relation for Photonsp. 83
Stability of Ground Statesp. 85
Bohr Modelp. 86
Fourier Transform and Uncertainty Relationsp. 88
Schrödinger Equationp. 90
Schrödinger Equation Examplep. 94
Dirac Delta Functionsp. 97
Wave Functions and Probabilityp. 99
Probability Currentp. 102
Time Separable Solutionsp. 103
Completeness for Particle Statesp. 104
Particle Operator Propertiesp. 107
Operator Rulesp. 110
Time Evolution and Expectation Valuesp. 112
Wrap-Up of Chapter 2p. 114
Problemsp. 115
Some One-Dimensional Solutions to the Schrödinger Equationp. 121
Introductionp. 121
The Infinite Square Well: Differential Solutionp. 123
The Infinite Square Well: Operator Solutionp. 129
The Finite Potential Barrier Step Potentialp. 134
The Harmonic Oscillatorp. 140
The Attractive Kronig-Penny Modelp. 149
Bound State and Scattering Solutionsp. 155
Problemsp. 156
Hilbert Space and Unitary Transformationsp. 161
Introduction and Notationp. 161
Inner and Outer Operator Productsp. 163
Operator-Matrix Relationshipp. 165
Hermitian Operators and Eigenketsp. 166
Gram-Schmidt Orthogonalization Processp. 168
Compatible Operatorsp. 170
Uncertainty Relations and Incompatible Operatorsp. 172
Simultaneously Measureable Operatorsp. 175
Unitary Transformations and Change of Basisp. 176
Coordinate Displacements and Unitary Transformationsp. 180
Schrödinger and Heisenburg Pictures of Time Evolutionp. 181
Free Gaussian Wave Packet in the Heisenberg Picturep. 184
Potentials and the Ehrenfest Theoremp. 185
Problemsp. 186
Three Static Approximation Methodsp. 191
Introductionp. 191
Time-Independent Perturbation Theoryp. 192
Examples of Time-Independent Perturbation Theoryp. 195
Aspects of Degenerate Perturbation Theoryp. 198
WKB Semiclassical Approximationp. 198
Use of the WKB Approximation in Barrier Penetrationp. 202
Use of the WKB Approximation in Bound Statesp. 204
Variational Methodsp. 207
Problemsp. 212
Generalization to Three Dimensionsp. 217
Cartesian Basis States and Wave Functions in Three Dimensionsp. 217
Position/Momentum Eigenket Generationp. 219
Example: Three-Dimensional Infinite Square Wellp. 222
Spherical Basis Statesp. 224
Orbital Angular Momentum Operatorp. 225
Effect of Angular Momentum on Basis Statesp. 226
Energy Eigenvalue Equation and Angular Momentump. 230
Complete Set of Observables for the Radial Schrödinger Equationp. 232
Specification of Angular Momentum Eigenstatesp. 234
Angular Momentum Eigenvectors and Spherical Harmonicsp. 240
Completeness and Other Properties of Spherical Harmonicsp. 245
Radial Eigenfunctionsp. 248
Problemsp. 248
Quantum Particles
The Three-Dimensional Radial Equationp. 255
Recap of the Situationp. 255
The Free Particlep. 257
The Infinite Spherical Well Potentialp. 264
The "Deuteron"p. 267
The Coulomb Potential: Initial Considerationsp. 280
The Coulomb Potential: 2-D Harmonic Oscillator Comparisonp. 283
The Confined Coulombic Modelp. 299
Problemsp. 307
Addition of Angular Momentap. 317
General Angular-Momentum Eigenstate Propertiesp. 317
Combining Angular Momenta for Two Systemsp. 319
Explicit Example of Adding Two Spin 1/2 Systemsp. 324
Explicit Example of Adding Orbital Angular Momentum and Spin 1/2p. 326
Hydrogen Atom and the Choice of Basis Statesp. 331
Hydrogen Atom and Perturbative Energy Shiftsp. 334
Problemsp. 338
Spin and Statisticsp. 343
The Connection between Spin and Statisticsp. 343
Building Wave Functions with Identical Particlesp. 344
Particle Occupation Basisp. 347
More on Fermi-Dirac Statisticsp. 352
Interaction Operator and Feynman Diagramsp. 354
Implications of Detailed Balancep. 357
Cubical Enclosures and Particle Statesp. 362
Maxwell-Boltzman Statisticsp. 364
Bose-Einstein Statisticsp. 366
Fermi-Dirac Statisticsp. 370
The Hartree-Fock Equationsp. 375
Problemsp. 379
Quantum Particle Scatteringp. 387
Introductionp. 387
The One-Dimensional Integral Schrödinger Equationp. 388
Reflection and Transmission Amplitudesp. 392
One-Dimensional Delta-Function Scatteringp. 393
Step-Function Potential Scatteringp. 396
The Born Seriesp. 402
The Three-Dimensional Integral Schrödinger Equationp. 404
The Helmholtz Equation and Plane Wavesp. 407
Cross Sections and the Scattering Amplitudep. 411
Scattering Phase Shiftsp. 412
Finite-Range Potential Scatteringp. 416
The Three-Dimensional Born Seriesp. 421
Identical Particle Scatteringp. 426
Proton-Proton Scatteringp. 430
Problemsp. 434
Connecting to the Standard Modelp. 443
Discrete Symmetriesp. 443
Parityp. 444
Time Reversalp. 448
Charge Conjugationp. 453
Particle Primerp. 454
Particle Interactionsp. 460
Quantum Electrodynamicsp. 461
Quantum Chromodynamicsp. 463
Weak Interactionsp. 468
Supersymmetryp. 472
Superstringsp. 474
Postludep. 477
Helpful Books on Particle and String Physicsp. 477
Problemsp. 478
Notation Comments and Comparisonsp. 485
Lattice Modelsp. 487
2-D Harmonic Oscillator Wave Function Normalizationp. 493
Allowed Standard Model Interactionsp. 495
The Ising Model and Morep. 497
Weak Flavor Mixingp. 509
Indexp. 523
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