Quantum Methods with Mathematica®

The first quantum mechanics text published that ties directly into a computer algebra system, this book exploits Mathematica(r) throughout for symbolic, numeric, and graphical computing. It is a work designed for computer interaction in an upper-division undergraduate or first-year graduate quantum mechanics course. It is also a toolbox for the practicing physicist seeking to automate a variety of algebraic and numerical tasks with the computer. The book is divided into two parts: "Systems in One Dimension" and "Quantum Dynamics." Part I emphasizes topics from a first-year course on quantum mechanics, while Part II includes more advanced topics. Although the text requires some familiarity with Mathematica, appendices are provided for gaining experience with the software and are referenced throughout the book. The text is task-oriented and integrated with numerous problems and exercises, with hints for working on the computer. James M. Feagin is a Professor of Physics at California State University, Fullerton. He was educated at Georgia Tech and the University of North Carolina, Chapel Hill, where he received a Ph.D. in theoretical physics in 1980. He is a Fellow of the Alexander von Humboldt Foundation and has served as visiting Professor at the University of Freiburg, Germany. Feagin is the author of numerous articles on collision physics and the dynamics of few-body systems. He has given a number of invited talks and hosted workshops on incorporating computers into the physics curriculum and is presently helping to introduce computing into the Introductory University Physics Project (IUPP) sponsored by the American Institute of Physics. The First Quantum Mechanics Text Published That Ties Directly Into A Computer Algebra System, This Book Exploits Mathematica Throughout For Symbolic, Numeric And Graphical Computing. It Is A Work Designed For Computer Interaction In An Upper-division Undergraduate Or First-year Graduate Quantum Mechanics Course. It Is Also A Toolbox For The Practicing Physicist Seeking To Automate A Variety Of Algebraic And Numerical Tasks With The Computer. -- Back Cover. The Book Is Divided Into Two Parts: Systems In One Dimension And Quantum Dynamics. Part I Emphasizes Topics From A First Year Course On Quantum Mechanics, While Part Ii Includes More Advanced Topics. Although The Text Requires Some Familiarity With Mathematica, Appendices Are Provided For Gaining Experience With The Software And Are Referenced Throughout The Book. The Text Is Task-oriented And Integrated With Numerous Problems And Exercises, With Hints For Working On The Computer. The 3.5 Diskette Included With This Book Contains All Of The Mathematica Input And Supporting Packages Appearing In The Text, So That The User Can Readily Enter And Analyze On The Computer Every Mathematical Step In The Book. The Diskette Can Be Read By Ibm Compatible, Macintosh, And Unix Computers. Foreword -- Preface -- Using This Book Interactively -- Pt. I. Systems In One Dimension. 1. Basic Wave Mechanics - 2. Particle In A Box - 3. Uncertainty Principle - 4. Free-particle Wavepacket - 5. Parity - 6. Harmonic Oscillator - 7. Variational Method And Perturbation Ideas - 8. Squeezed States - 9. Basic Matrix Mechanics - 10. Partial Exact Diagonalization - 11. Momentum Representation - 12. Lattice Representation - 13. Morse Oscillator - 14. Potential Scattering -- Pt. Ii. Quantum Dynamics. 15. Quantum Operators - 16. Angular Momentum - 17. Angular Momentum Coupling - 18. Coordinate And Momentum Representations - 19. Angular Momentum In Spherical Coordinates - 20. Hydrogen Atom Schrodinger Equation - 21. Wavefunctions From The Runge-lenz Algebra -- Appendix I. Mathematica Quick View -- Appendix Ii. Notebooks And Basic Tools -- Appendix Iii. Home Improvement -- Appendix Iv. Quantum Packages -- Appendix V. Grad, Div, Curl -- Bibliography -- Index. James M. Feagin. Includes Diskette. System Requirements For Computer Disk (mathematica): Ibm Compatible, Macintosh, And Unix Computers. Includes Bibliographical References (p. [465]-468) And Index. Quantum Methods with Mathematica......Page 2 Foreword......Page 4 Preface......Page 6 Contents......Page 10 PART I Systems in One Dimension......Page 16 Systems in One Dimension......Page 18 1 Basic Wave Mechanics......Page 20 2 Particle in a Box......Page 28 3 Uncertainty Principle......Page 46 4 Free-ParticleWavepacket......Page 50 5 Parity......Page 60 6 Harmonic Oscillator......Page 66 7 Variational Method and Perturbation Ideas......Page 90 8 Squeezed States......Page 100 9 Basic Matrix Mechanics......Page 116 10 Partial Exact Diagonalization......Page 122 11 Momentum Representation......Page 136 12 Lattice Representation......Page 160 13 Morse Oscillator......Page 204 14 Potential Scattering......Page 220 PART II Quantum Dynamics......Page 250 Quantum Dynamics......Page 252 15 Quantum Operators......Page 254 16 Angular Momentum......Page 268 17 Angular Momentum Coupling......Page 282 18 Coordinate and Momentum Representations......Page 302 19 Angular Momentumin Spherical Coordinates......Page 318 20 Hydrogen Atom Schrodinger Equation......Page 338 21 Wavefunctions from the Runge-LenzAlgebra......Page 360 Appendix I Mathematica Quick View......Page 384 Appendix II Notebooks and Basic Tools......Page 386 Appendix III Home Improvement......Page 398 Appendix IV Quantum Packages......Page 438 Appendix V Grad, Div, Curl......Page 448 Bibliography......Page 480 Index......Page 484 This package of book and diskette can be used in an introductory quantum mechanics course, either in conventional or computer laboratory-based settings. It provides those new to Mathematica with an explanation of usage and syntax, and contains numerous problems and exercises.