
Quantum Mechanics
From Basic Principles to Numerical Methods and Applications
By: Louis Marchildon
Hardcover | 13 May 2002
At a Glance
580 Pages
23.5 x 16.51 x 4.45
Hardcover
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From the reviews:
"This is an interesting a valuable book for someone who wants to obtain a solid understanding of the fundamental aspects of quantum mechanics, an appreciation of some aspects of the numerical solution of practical applications, and an introduction or better to a very broad spectrum of topics."-Chemistry in Asutralia Magazine of the Royal Astralian Chemical Institute
"This is an expository book on Quantum Mechanics. The exposition largely develops around the central notion of state space. ... Although the exposition is largely self contained, numerous references are given to books and research papers. This is a very useful book for undergraduate and graduate students who study Quantum Mechanics." (T. C. Mohan, Zentralblatt MATH, Vol. 1033 (8), 2004)
"There are some excellent and classic texts on quantum mechanics (QM) ... . The present monograph represents an attempt to rewrite and rearrange the outlook and topics ... . Overall the book offers a rich mix of topics and is highly readable. The exercises at the end of each chapter represent a reasonable collection for the students to test their comprehension and assimilation of the subject matter. It is a welcome addition to the large number of books on QM." (Mayer Humi, Mathematical Reviews, 2003 m)
"His 'exposition largely develops round the central notion of state space'. ... This could be a useful book for an advanced graduate course or theoretical specialists and a useful reference for others ... ." (Alastair Rae, Times Higher Education supplement, May, 2003)
"I like this book, and I'll probably use it as a reference and resource for my Honours year quantum mechanics course. ... One of the strengths of this book is the thorough treatment of atomic theory ... ." (Craig Savage, The Physicist, Vol. 39 (6), 2002)
"This is an interesting and valuable book for someone who wants to obtain a solid understanding of the fundamental aspects of quantum mechanics ... . For those higher year undergraduate and graduate students of physical and theoretical chemistry who want to teach themselves quantum mechanics, this book might provide a better route than other standard texts." (Michael Collins, Chemistry in Australia, January/February, 2003)
| A Crisis in Classical Physics | p. 1 |
| The Reality of Atoms | p. 1 |
| The Reality of Field | p. 3 |
| The Discreteness of Energy | p. 4 |
| The Nature of Atomic Objects | p. 8 |
| At the Threshold of the Quantum Revolution | p. 9 |
| Finite-Dimensional Vector Spaces | p. 11 |
| Vector Spaces and Scalar Product | p. 11 |
| Operators | p. 14 |
| Eigenvalues and Eigenvectors | p. 16 |
| Matrix Representation of Linear Operators | p. 17 |
| Spectral Decomposition | p. 21 |
| Functions of an Operator | p. 23 |
| Commuting Operators | p. 25 |
| Direct Sum of Vector Spaces | p. 26 |
| Exercises | p. 27 |
| Finite-Dimensional State Spaces | p. 31 |
| The State of a System | p. 31 |
| Dynamical Variables | p. 33 |
| Hamiltonian | p. 38 |
| The Schrödinger Equation | p. 38 |
| Time-Independent Hamiltonian | p. 41 |
| Solution of the Schrödinger Equation | p. 43 |
| Commuting Operators | p. 44 |
| The Hydrogen Molecular Ion | p. 45 |
| Exercises | p. 48 |
| Spin and Magnetic Moment | p. 53 |
| The Stern-Gerlach Experiment | p. 53 |
| Spatial Rotations | p. 56 |
| Generators of Rotation | p. 58 |
| Spin, Magnetic Moment and the Zeeman Effect | p. 62 |
| The Larmor Precession | p. 65 |
| Spin 1/2 | p. 66 |
| Exercises | p. 69 |
| Particle in One Dimension | p. 71 |
| Basis Vectors |x〉 | p. 71 |
| Position, Momentum and Energy | p. 73 |
| State Space | p. 76 |
| The Schrödinger Equation | p. 81 |
| Square Well Potential | p. 83 |
| Square Potential Barrier | p. 87 |
| The Harmonic Oscillator | p. 88 |
| Evolution Operator and Wave Packets | p. 93 |
| Appendix | p. 97 |
| The Dirac Delta Function | p. 97 |
| Infinite-Dimensional Vector Spaces | p. 100 |
| Hermite Polynomials | p. 101 |
| Exercises | p. 104 |
| The Interpretation of Quantum Mechanics | p. 109 |
| Formalism and Interpretation Rules | p. 109 |
| Interpretation of the State Vector | p. 111 |
| State Preparation and Measurement | p. 115 |
| The Heisenberg Uncertainty Principle | p. 118 |
| Complementarity | p. 122 |
| Quantum Mechanics and Classical Mechanics | p. 123 |
| Exercises | p. 125 |
| Particle in Three Dimensions | p. 127 |
| State Space and Schrödinger's Equation | p. 127 |
| Probability Current | p. 131 |
| Angular Momentum | p. 134 |
| Spherically Symmetric Potential | p. 138 |
| r−1 Potential | p. 140 |
| Spherical Square Well | p. 143 |
| Electromagnetic Field | p. 145 |
| Gauge Transformation | p. 148 |
| Appendix | p. 151 |
| Legendre Polynomials and Spherical Harmonics | p. 151 |
| Laguerre Polynomials | p. 154 |
| Bessel Functions | p. 155 |
| Exercises | p. 158 |
| Numerical Solution | p. 163 |
| Finite-Difference Equation | p. 163 |
| Discrete Spectrum in One Dimension | p. 166 |
| Box Normalization | p. 170 |
| Discrete Spectrum in Three Dimensions | p. 173 |
| Phase Shifts | p. 177 |
| Exercises | p. 180 |
| The Central-Field Model | p. 183 |
| The Hamiltonian of an Atom | p. 183 |
| The Hydrogen Atom and Hydrogen-Like Ions | p. 187 |
| The Central Field | p. 188 |
| The Thomas-Fermi Equation | p. 190 |
| The Periodic Table of Elements | p. 193 |
| Self-Consistent Field | p. 195 |
| Validity of the Central-Field Model | p. 198 |
| Exercises | p. 202 |
| Stationary Perturbations | p. 205 |
| Small Perturbation | p. 205 |
| Nondegenerate Energy | p. 207 |
| Degenerate Energy | p. 209 |
| Spatial Extension of the Atomic Nucleus | p. 211 |
| Dipole Moment of Atoms and Stark Effect | p. 213 |
| Van der Waals Forces | p. 215 |
| Rotation and Vibration of Diatomic Molecules | p. 218 |
| Exercises | p. 221 |
| Stationary Scattering States | p. 225 |
| Scattering Cross Section | p. 225 |
| Stationary Scattering States | p. 227 |
| Green's Operators and Functions | p. 229 |
| Scattering Integral Equation | p. 234 |
| The Born Approximation | p. 235 |
| Partial Waves and Phase Shifts | p. 238 |
| Hard Sphere and Spherical Square Well | p. 242 |
| Analytic Properties of Partial Waves | p. 244 |
| Scattering by Many Identical Centers | p. 248 |
| Exercises | p. 252 |
| The Density Operator | p. 255 |
| Pure State | p. 255 |
| Statistical Mixture | p. 257 |
| Tensor Product of State Spaces | p. 259 |
| Description of a Subsystem | p. 261 |
| Application to Statistical Physics | p. 264 |
| Consistent Histories | p. 267 |
| Exercises | p. 271 |
| Symmetry of the Hamiltonian | p. 275 |
| Symmetry Group | p. 275 |
| Space Inversion, Rotations and Translations | p. 277 |
| General Properties of Groups | p. 279 |
| Matrix Representation of a Group | p. 281 |
| Finite Groups | p. 284 |
| Time Reversal | p. 290 |
| Lie Groups | p. 292 |
| Spatial Translations | p. 296 |
| Exercises | p. 299 |
| Rotations and Angular Momentum | p. 305 |
| The Rotation Group | p. 305 |
| Finite Rotations | p. 310 |
| D Matrices as Wave Functions | p. 315 |
| Interaction of Two Angular Momenta | p. 319 |
| Total Angular Momentum | p. 321 |
| Clebsch-Gordan Coefficients | p. 323 |
| The Wigner-Eckart Theorem | p. 327 |
| Enlarged Symmetry | p. 329 |
| Exercises | p. 333 |
| Dirac's Relativistic Equation | p. 337 |
| The Lorentz Group | p. 337 |
| The Dirac Equation | p. 342 |
| Plane-Wave Solution | p. 344 |
| Properties of the Dirac Equation | p. 346 |
| Electron in an Electromagnetic Field | p. 349 |
| r−1 Potential | p. 353 |
| Exercises | p. 358 |
| The Path Integral | p. 361 |
| Propagator and Path Integral | p. 361 |
| Convergence of Path Integrals | p. 366 |
| The Semiclassical Approximation | p. 369 |
| WKB Wave Functions | p. 374 |
| Turning Point | p. 377 |
| The Bohr-Sommerfeld Rule | p. 380 |
| Potential Barrier | p. 382 |
| Classical Evolution | p. 384 |
| Exercises | p. 387 |
| Atomic Orbitals | p. 391 |
| The Variational Method | p. 391 |
| The Ground-State Energy of the Helium Atom | p. 393 |
| Antisymmetric Wave Functions | p. 396 |
| The Hartree-Fock Equations | p. 400 |
| Using the Hartree-Fock Equations | p. 406 |
| Exercises | p. 410 |
| Atomic Terms and Multiplets | p. 413 |
| LS Coupling | p. 413 |
| Atomic Wave Functions | p. 417 |
| Average Energy of a Configuration | p. 422 |
| Energy of Atomic Multiplets | p. 427 |
| Spin-Orbit Interaction | p. 433 |
| The Zeeman Effect | p. 437 |
| Configuration Interaction | p. 440 |
| Exercises | p. 442 |
| Semiclassical Radiation Theory | p. 445 |
| Harmonic Perturbation | p. 445 |
| Transition to the Continuous Spectrum | p. 449 |
| Transition to the Discrete Spectrum | p. 453 |
| Spontaneous Emission | p. 457 |
| Electric Dipole Transitions | p. 459 |
| Higher-Order Transitions | p. 462 |
| The Shape of Spectral Lines | p. 465 |
| Exercises | p. 467 |
| Molecules | p. 471 |
| The Born-Oppenheimer Approximation | p. 471 |
| Molecular Orbitals | p. 475 |
| Electronic Terms of Diatomic Molecules | p. 481 |
| Rotation and Vibration of Diatomic Molecules | p. 485 |
| Electric Dipole Transitions | p. 488 |
| Polyatomic Molecules | p. 493 |
| Exercises | p. 496 |
| Long-Distance Correlations and Measurement | p. 499 |
| Einstein, Podolsky and Rosen | p. 499 |
| The Bell Inequality | p. 502 |
| Quantum Mechanics and Relativistic Locality | p. 505 |
| The Measurement Problem | p. 508 |
| Search for a Solution | p. 513 |
| Decoherence | p. 517 |
| True Propositions and Reliable Propositions | p. 520 |
| Answers to Selected Exercises | p. 525 |
| References | p. 537 |
| Index | p. 549 |
| Table of Contents provided by Publisher. All Rights Reserved. |
ISBN: 9783540433422
ISBN-10: 3540433422
Series: Advanced Texts in Physics
Published: 13th May 2002
Format: Hardcover
Language: English
Number of Pages: 580
Audience: College, Tertiary and University
Publisher: Springer Nature B.V.
Country of Publication: DE
Dimensions (cm): 23.5 x 16.51 x 4.45
Weight (kg): 1.01
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