Résumé
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.
Contents
Part I: Systems in One Dimension
- Basic Wave Mechanics: equations of motion, stationary states, a well-posed problem, time-development operator, extra dimensions
- Particle in a Box: analytical eigenfunctions, numerical eigenfunctions, two basic properties, rectangular wave, quantum rattle, measurements
- Uncertainty Principle
- Free-Particle Wavepacket: stationary wavepacket, moving wavepacket
- Parity
- Harmonic Oscillator: scaled Schrödinger equation, method of solution,energy spectrum, Hermite polynomials, hypergeometric functions, normalized HO wavefunctions, raising and lowering operators
- Variational Method and Perturbation Ideas: HO ground state variationally, HO excited state variationally, model Hamiltonian, first-order perturbation energy
- Squeezed States: eigenfunction expansion, time evolution, Newton's laws, quasi-classical states
- Basic Matrix Mechanics: HO coordinate and momentum, matrix elements, HO coordinate and momentum matrices, HO Hamiltonian matrix
- Partial Exact Diagonalization: model-Hamiltonian matrix, matrix eigenvalues and eigenvectors, perturbed eigenfunctions, local energy, pseudo states and resonances, diagonalization
- Momentum Representation: tools, momentum wavefunctions, conventions, HO momentum wavefunctions, Dirac Delta function, momentum operator, local energy, coordinate operator, momentum-space Hamiltonian, exponential operators, more squeezed states
- Lattice Representation: coordinate lattice, momentum lattice, discrete Fourier transforms, local energy, FFT, wavepacket propagation, quantum diffusion
- Morse Oscillator: Kummer's equation, eigenenergies, eigenfunctions, normalization, hypergeometric integrals
- Potential Scattering: numerical solution, scattering amplitudes, resonance hunting, radial wavefunctions, resonance parameterization, wavepacket impact
- Quantum Operators: commutator algebras, two-body relative coordinates, Bra-Ket formalism, harmonic oscillator spectrum
- Angular Momentum: angular momentum spectrum, matrix representation, new axis of quantization, quantum rotation matrix
- Angular Momentum Coupling: spin and orbital coupling, total angular momentum spectrum, Clebsch Gordanary, Wigner 3j symbols, recoupling coefficients
- Coordinate and Momentum Representations: position and momentum operators, commutation relations, angular momentum in Cartesian coordinates, rotational symmetry, dynamical symmetry, Runge-Lenz vector, hydrogen atom spectrum
- Angular Momentum in Spherical Coordinates: spherical harmonics, new axis of quantization, quantum rotation matrix
- Hydrogen Atom Schrödinger Equation: seperation in spherical coordinates, bound-state wavefunctions, parity, continuum wavefunctions, separation in parabolic coordinates
- Wavefunctions from the Runge-Lenz Algebra: raising and lowering operators, top-rung states, down the ladder, connection with the parabolic separation, linear Stark effect, connection with the spherical separation
- Mathematica Quick View
- Notebooks and Basic Tools: projectile motion ignoring air resistance
- Home Improvement: functions, algebra, computing
- Quantum Packages: Quantum`Clebsch`, Quantum`integExp`, Quantum`integGauss`, Quantum`NonCommutativeMultiply`, Quantum`PowerTools`, Quantum`QuantumRotations`, Quantum`QuickReIm`, QuantumTrigonometry`
- Grad, Div, Curl: vector products, Cartesian coordinates, curvilinear coordinates, spherical coordinates
L'auteur - James M. Feagin
Jim Feagin is 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 preesently helping to introduce computing into the Introductory University Physics Project (IUPP) sponsored by the American Institute of Physics.
Caractéristiques techniques
| PAPIER | |
| Éditeur(s) | Springer |
| Auteur(s) | James M. Feagin |
| Parution | 30/01/2002 |
| Nb. de pages | 782 |
| Format | 17,8 x 23,4 |
| Couverture | Broché |
| Poids | 800g |
| Intérieur | Noir et Blanc |
| EAN13 | 9780387953656 |
| ISBN13 | 978-0-387-95365-6 |
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