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. The teaching and learning of nonrelativistic quantum mechanics have in recent years been profoundly affected by two developments. First, advances in experimental technique, especially in quantum optics and electronics and in neutron interferometry, have turned many quantum phenomena and "thought experiments," which previously had only been the subject of hypothetical inferences, into laboratory reality. The other line of progress has been, after much premature advertising, the advent of computational physics as a tool of the trade that now belongs, and fits, into every student's bag. Quantum Methods with Mathematica® places itself comfortably four-square in our contemporary culture by using the full technology of Mathematica as its pedagogic environment. I confess that I approached the manuscript of this text with apprehension, fearing that, with no previous exposure to Mathematica and well past the nimble age, I might quickly come to grief and frustration. As I write this, I have survived the course, and I have learned the wonders (and some of the foibles) of Mathematica, as well as some new things about quantum mechanics. And, under Jim Feagin's deft guidance, the experience has been fun! Title Page Foreword Preface Using This Book Interactively Table of Contents Part 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 Part 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 Schrödinger 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 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.