
Foundations of Quantum Physics
By:Â Charles E. Burkhardt, Jacob J. Leventhal
Hardcover | 19 September 2008
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552 Pages
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Our book is meant to be a text for a first undergraduate course in quantum physics. Both of us have taught this course numerous times and have used several different texts, some of them excellent. Obviously, though, there are changes we would make and that is the reason we are writing this book.
Two of the most widely used books for this course are the excellent texts by Griffiths (Prentice-Hall) and Gasiorowicz (Wiley), both of which we have used. Another, which neither of us has used but both of us are familiar with, is by Liboff (Addison-Wesley). While we find much to like about these books, there are matters of style, order of presentation and included subject matter that we obviously prefer. We do not wish our comments to be taken as criticism of other books but merely as a statement of our own preferences and the reasons that we believe our style and method can be helpful to students and instructors.
We wish to avoid a modern trend in textbooks that is to condense and compress these texts into ever smaller and smaller size. We are not sure whether this trend is to lower the cost of the book or to make the book seem less formidable to the student, but we believe that a textbook should be more than a one or two semester acquaintance. This is especially true for a course such as quantum mechanics which is likely taken by physics majors who will use the subject for the rest of their careers. We therefore believe that a textbook can (and should) contain material that an instructor will choose to omit. In keeping with this theme, there are topics included that are not normally covered in introductory textbooks, not necessarily too advanced, but not usually covered. Perhaps in years to come this student, now working as a physicist, is interested in the subject that was skipped during the course. He/she knows where to find the material in a book that is quite familiar to him/her. Both of us have many such books in our personal libraries. It seems as if modern physics texts are not built to be long term reference books. This is just our observation and we would like our book to have a oestaying powera and be long term companions.
Industry Reviews
From the reviews:
"This book is meant to be used for a first course in quantum mechanics and assumes that the student has taken a modern physics course and has had mathematics through differential equations. ... The book reviews how to sketch wave functions for a variety of 1-D potentials and addresses the standard calculations for special cases. ... Overall, this is an excellent book ... . Summing Up: Highly recommended. Upper-division undergraduates." (E. Kincanon, Choice, Vol. 46 (8), April, 2009)
"This textbook provides an introduction to quantum mechanics at an elementary level. ... The presentation of the topics is very good and pedagogical. ... Finally, many exercises and their solutions ... are given. All in all, this book provides an excellent introduction to the field of quantum physics. It will be very useful to beginning students in quantum mechanics, and also to lecturers on this topic. It is highly recommended as a basis for a course, or even for self-study." (Axel Maas, Mathematical Reviews, Issue 2009 m)
| Preface | p. vii |
| Introduction | p. 1 |
| Early Experiments | p. 1 |
| The Photoelectric Effect | p. 1 |
| The Franck-Hertz Experiment | p. 3 |
| Atomic Spectroscopy | p. 5 |
| Electron Diffraction Experiments | p. 7 |
| The Compton Effect | p. 8 |
| Early Theory | p. 10 |
| The Bohr Atom and the Correspondence Principle | p. 10 |
| The de Broglie Wavelength | p. 18 |
| The Uncertainty Principle | p. 19 |
| The Compton Wavelength Revisited | p. 21 |
| The Classical Radius of the Electron | p. 23 |
| Units | p. 24 |
| Retrospective | p. 25 |
| References | p. 25 |
| Problems | p. 25 |
| Elementary Wave Mechanics | p. 27 |
| What is Doing the Waving? | p. 27 |
| A Gedanken Experiment-Electron Diffraction Revisited | p. 27 |
| The Wave Function | p. 28 |
| Finding the Wave Function-the Schrodinger Equationo | p. 29 |
| The Equation of Continuity | p. 32 |
| Separation of the Schrodinger Equation-Eigenfunctions | p. 33 |
| The General Solution to the Schrodinger Equation | p. 35 |
| Stationary States and Bound States | p. 38 |
| Characteristics of the Eigenfunctions [psi subscript n] (x) | p. 38 |
| Retrospective | p. 43 |
| Problems | p. 44 |
| Quantum Mechanics in One Dimension-Bound States I | p. 47 |
| Simple Solutions of the Schrodinger Equation | p. 47 |
| The Infinite Square Well-the "Particle-in-a-Box" | p. 47 |
| The Harmonic Oscillator | p. 56 |
| Penetration of the Classically Forbidden Region | p. 69 |
| The Infinite Square Well with a Rectangular Barrier Inside | p. 73 |
| Retrospective | p. 77 |
| References | p. 77 |
| Problems | p. 78 |
| Time-Dependent States in One Dimension | p. 83 |
| The Ehrenfest Equations | p. 83 |
| The Free Particle | p. 85 |
| Quantum Representation of Particles-Wave Packets | p. 86 |
| Momentum Representation of the Operator x | p. 90 |
| The Dirac [delta]-function | p. 91 |
| Parseval's Theorem | p. 93 |
| The Harmonic Oscillator Revisited-Momentum Eigenfunctions | p. 94 |
| Motion of a Wave Packet | p. 96 |
| Case I. The Free Packet/Particle | p. 98 |
| Case II. The Packet/Particle Subjected to a Constant Field | p. 101 |
| Case III. The Packet/Particle Subjected to a Harmonic Oscillator Potential | p. 104 |
| Retrospective | p. 108 |
| Problems | p. 109 |
| Stationary States in One Dimension II | p. 113 |
| The Potential Barrier | p. 113 |
| The Potential Step | p. 121 |
| The Finite Square Well-Bound States | p. 123 |
| The Morse Potential | p. 130 |
| The Linear Potential | p. 139 |
| The WKB Approximation | p. 145 |
| The Nature of the Approximation | p. 145 |
| The Connection Formulas for Bound States | p. 148 |
| A Bound State Example-the Linear Potential | p. 155 |
| Tunneling | p. 158 |
| Comparison with a Rectangular Barrier | p. 162 |
| A Tunneling Example-Predissociation | p. 163 |
| References | p. 165 |
| Problems | p. 165 |
| The Mechanics of Quantum Mechanics | p. 169 |
| Abstract Vector Spaces | p. 169 |
| Matrix Representation of a Vector | p. 171 |
| Dirac Notation for a Vector | p. 172 |
| Operators in Quantum Mechanics | p. 173 |
| The Eigenvalue Equation | p. 179 |
| Properties of Hermitian Operators and the Eigenvalue Equation | p. 180 |
| Properties of Commutators | p. 186 |
| The Postulates of Quantum Mechanics | p. 189 |
| Listing of the Postulates | p. 189 |
| Discussion of the Postulates | p. 190 |
| Further Consequences of the Postulates | p. 198 |
| Relation Between the State Vector and the Wave Function | p. 200 |
| The Heisenberg Picture | p. 202 |
| Spreading of Wave Packets | p. 207 |
| Spreading in the Heisenberg Picture | p. 207 |
| Spreading in the Schrodinger Picture | p. 211 |
| Retrospective | p. 216 |
| References | p. 217 |
| Problems | p. 217 |
| Harmonic Oscillator Solution Using Operator Methods | p. 219 |
| The Algebraic Method | p. 219 |
| The Schrodinger Picture | p. 219 |
| Matrix Elements | p. 224 |
| The Heisenberg Picture | p. 227 |
| Coherent States of the Harmonic Oscillator | p. 229 |
| Retrospective | p. 236 |
| Reference | p. 236 |
| Problems | p. 237 |
| Quantum Mechanics in Three Dimensions-Angular Momentum | p. 239 |
| Commutation Relations | p. 240 |
| Angular Momentum Ladder Operators | p. 241 |
| Definitions and Commutation Relations | p. 241 |
| Angular Momentum Eigenvalues | p. 242 |
| Vector Operators | p. 247 |
| Orbital Angular Momentum Eigenfunctions-Spherical Harmonics | p. 249 |
| The Addition Theorem for Spherical Harmonics | p. 257 |
| Parity | p. 259 |
| The Rigid Rotor | p. 260 |
| Another Form of Angular Momentum-Spin | p. 262 |
| Matrix Representation of the Spin Operators and Eigenkets | p. 266 |
| The Stern-Gerlach Experiment | p. 270 |
| Addition of Angular Momenta | p. 273 |
| Examples of Angular Momentum Coupling | p. 277 |
| Spin and Identical Particles | p. 285 |
| The Vector Model of Angular Momentum | p. 292 |
| Retrospective | p. 294 |
| References | p. 294 |
| Problems | p. 294 |
| Central Potentials | p. 297 |
| Separation of the Schrodinger Equation | p. 298 |
| The Effective Potential | p. 300 |
| Degeneracy | p. 302 |
| Behavior of the Wave Function for Small and Large Values of r | p. 304 |
| The Free Particle in Three Dimensions | p. 305 |
| The Infinite Spherical Square Well | p. 308 |
| The Finite Spherical Square Well | p. 309 |
| The Isotropic Harmonic Oscillator | p. 316 |
| Cartesian Coordinates | p. 317 |
| Spherical Coordinates | p. 319 |
| The Morse Potential in Three Dimensions | p. 339 |
| Retrospective | p. 343 |
| References | p. 344 |
| Problems | p. 344 |
| The Hydrogen Atom | p. 347 |
| The Radial Equation-Energy Eigenvalues | p. 347 |
| Degeneracy of the Energy Eigenvalues | p. 352 |
| The Radial Equation-Energy Eigenfunctions | p. 354 |
| The Complete Energy Eigenfunctions | p. 361 |
| Retrospective | p. 362 |
| References | p. 362 |
| Problems | p. 362 |
| Angular Momentum-Encore | p. 365 |
| The Classical Kepler Problem | p. 365 |
| The Quantum Mechanical Kepler Problem | p. 367 |
| The Action of A[subscript +] | p. 371 |
| Retrospective | p. 372 |
| References | p. 372 |
| Problems | p. 372 |
| Time-Independent Approximation Methods | p. 375 |
| Perturbation Theory | p. 375 |
| Nondegenerate Perturbation Theory | p. 375 |
| Degenerate Perturbation Theory | p. 382 |
| The Variational Method | p. 390 |
| Problems | p. 393 |
| Applications of Time-Independent Approximation Methods | p. 397 |
| Hydrogen Atoms | p. 397 |
| Breaking the Degeneracy-Fine Structure | p. 397 |
| Spin-Orbit Coupling and the Shell Model of the Nucleus | p. 409 |
| Helium Atoms | p. 411 |
| The Ground State | p. 411 |
| Excited States | p. 417 |
| Multielectron Atoms | p. 422 |
| Retrospective | p. 427 |
| References | p. 428 |
| Problems | p. 428 |
| Atoms in External Fields | p. 431 |
| Hydrogen Atoms in External Fields | p. 431 |
| Electric Fields-the Stark Effect | p. 431 |
| Magnetic Fields-The Zeeman Effect | p. 436 |
| Multielectron Atoms in External Magnetic Fields | p. 442 |
| Retrospective | p. 446 |
| References | p. 446 |
| Problems | p. 446 |
| Time-Dependent Perturbations | p. 449 |
| Time Dependence of the State Vector | p. 449 |
| Two-State Systems | p. 452 |
| Harmonic Perturbation-Rotating Wave Approximation | p. 452 |
| Constant Perturbation Turned On at t = 0 | p. 455 |
| Time-Dependent Perturbation Theory | p. 457 |
| Two-state Systems Using Perturbation Theory | p. 459 |
| Harmonic Perturbation | p. 459 |
| Constant Perturbation Turned On at t = 0 | p. 462 |
| Extension to Multistate Systems | p. 464 |
| Harmonic Perturbation | p. 464 |
| Constant Perturbation Turned On at t = 0 | p. 465 |
| Transitions to a Continuum of States-The Golden Rule | p. 465 |
| Interactions of Atoms with Radiation | p. 468 |
| The Nature of Electromagnetic Transitions | p. 469 |
| The Transition Rate | p. 470 |
| The Einstein Coefficients-Spontaneous Emission | p. 473 |
| Selection Rules | p. 476 |
| Transition Rates and Lifetimes | p. 480 |
| References | p. 483 |
| Problems | p. 483 |
| Answers to Problems | p. 485 |
| Chapter 1 | p. 485 |
| Chapter 2 | p. 485 |
| Chapter 3 | p. 487 |
| Chapter 4 | p. 489 |
| Chapter 5 | p. 489 |
| Chapter 6 | p. 490 |
| Chapter 7 | p. 491 |
| Chapter 8 | p. 491 |
| Chapter 9 | p. 492 |
| Chapter 10 | p. 492 |
| Chapter 11 | p. 493 |
| Chapter 12 | p. 493 |
| Chapter 13 | p. 494 |
| Chapter 14 | p. 495 |
| Chapter 15 | p. 496 |
| Useful Constants | p. 497 |
| Energy Units | p. 499 |
| Useful Formulas | p. 501 |
| Greek Alphabet | p. 503 |
| Acronyms | p. 505 |
| [Gamma]-Functions | p. 507 |
| Integral [Gamma]-Functions | p. 507 |
| Half-Integral [Gamma]-Functions | p. 507 |
| Useful Integrals | p. 509 |
| Useful Series | p. 511 |
| Taylor Series | p. 511 |
| Binomial Expansion | p. 511 |
| Gauss' Trick | p. 512 |
| Fourier Integrals | p. 515 |
| Commutator Identities | p. 519 |
| General Identities | p. 519 |
| Quantum Mechanical Identities | p. 519 |
| Miscellaneous Operator Relations | p. 521 |
| Baker-Campbell-Hausdorff (BCH) Formula | p. 521 |
| Translation Operator | p. 522 |
| Index | p. 525 |
| Table of Contents provided by Ingram. All Rights Reserved. |
ISBN: 9780387776514
ISBN-10: 0387776516
Published: 19th September 2008
Format: Hardcover
Language: English
Number of Pages: 552
Audience: Professional and Scholarly
Publisher: Springer Nature B.V.
Country of Publication: US
Dimensions (cm): 24.13 x 16.51 x 3.18
Weight (kg): 0.89
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