Quantum Mechanics Classical Results, Modern Systems, and Visualized Examples 2/e

Name: Quantum Mechanics Classical Results, Modern Systems, and Visualized Examples 2/e | Classical Results, Modern Systems, and Visualized Examples
Brand: Oxford University Press
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Classical Results, Modern Systems, and Visualized Examples

ROBINETT RICHARD(Autor*in)

Oxford University Press

1. Auflage

Erschienen am 13. April 2006

722 Seiten

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978-0-19-152398-4 (ISBN)

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Inhalt

Intro
CONTENTS
Part I: The Quantum Paradigm
1 A First Look at Quantum Physics
1.1 How this Book Approaches Quantum Mechanics
1.2 Essential Relativity
1.3 Quantum Physics: h as a Fundamental Constant
1.4 Semiclassical Model of the Hydrogen Atom
1.5 Dimensional Analysis
1.6 Questions and Problems
2 Classical Waves
2.1 The Classical Wave Equation
2.2 Wave Packets and Periodic Solutions
2.3 Fourier Transforms
2.4 Inverting the Fourier transform: the Dirac d-function
2.5 Dispersion and Tunneling
2.6 Questions and Problems
3 The Schrödinger Wave Equation
3.1 The Schrödinger Equation
3.2 Plane Waves and Wave Packet Solutions
3.3 "Bouncing" Wave Packets
3.4 Numerical Calculation of Wave Packets
3.5 Questions and Problems
4 Interpreting the Schrödinger Equation
4.1 Introduction to Probability
4.2 Probability Interpretation of the Schrödinger Wavefunction
4.3 Average Values
4.4 Real Average Values and Hermitian Operators
4.5 The Physical Interpretation of f(p)
4.6 Energy Eigenstates, Stationary States, and the Hamiltonian Operator
4.7 The Schrödinger Equation in Momentum Space
4.8 Commutators
4.9 The Wigner Quasi-Probability Distribution
4.10 Questions and Problems
5 The Infinite Well: Physical Aspects
5.1 The Infinite Well in Classical Mechanics: Classical Probability Distributions
5.2 Stationary States for the Infinite Well
5.3 The Asymmetric Infinite Well
5.4 Time-Dependence of General Solutions
5.5 Questions and Problems
6 The Infinite Well: Formal Aspects
6.1 Dirac Bracket Notation
6.2 Eigenvalues of Hermitian Operators
6.3 Orthogonality of Energy Eigenfunctions
6.4 Expansions in Eigenstates
6.5 Expansion Postulate and Time-Dependence
6.6 Parity
6.7 Simultaneous Eigenfunctions
6.8 Questions and Problems
7 Many Particles in the Infinite Well: The Role of Spin and Indistinguishability
7.1 The Exclusion Principle
7.2 One-Dimensional Systems
7.3 Three-Dimensional Infinite Well
7.4 Applications
7.5 Questions and Problems
8 Other One-Dimensional Potentials
8.1 Singular Potentials
8.2 The Finite Well
8.3 Applications to Three-Dimensional Problems
8.4 Questions and Problems
9 The Harmonic Oscillator
9.1 The Importance of the Simple Harmonic Oscillator
9.2 Solutions for the SHO
9.3 Experimental Realizations of the SHO
9.4 Classical Limits and Probability Distributions
9.5 Unstable Equilibrium: Classical and Quantum Distributions
9.6 Questions and Problems
10 Alternative Methods of Solution and Approximation Methods
10.1 Numerical Integration
10.2 The Variational or Rayleigh-Ritz Method
10.3 The WKB method
10.4 Matrix Methods
10.5 Perturbation Theory
10.6 Questions and Problems
11 Scattering
11.1 Scattering in One-Dimensional Systems
11.2 Scattering from a Step Potential
11.3 Scattering from the Finite Square Well
11.4 Applications of Quantum Tunneling
11.5 Questions and Problems
12 More Formal Topics
12.1 Hermitian Operators
12.2 Quantum Mechanics, Linear Algebra, and Vector Spaces
12.3 Commutators
12.4 Uncertainty Principles
12.5 Time-Dependence and Conservation Laws in Quantum Mechanics
12.6 Propagators
12.7 Timescales in Bound State Systems: Classical Period and Quantum Revival Times
12.8 Questions and Problems
13 Operator and Factorization Methods for the Schrödinger Equation
13.1 Factorization Methods
13.2 Factorization of the Harmonic Oscillator
13.3 Creation and Annihilation Operators
13.4 Questions and Problems
14 Multiparticle Systems
14.1 Generalities
14.2 Separable Systems
14.3 Two-Body Systems
14.4 Spin Wavefunctions
14.5 Indistinguishable Particles
14.6 Questions and Problems
Part II: The Quantum World
15 Two-Dimensional Quantum Mechanics
15.1 2D Cartesian Systems
15.2 Central Forces and Angular Momentum
15.3 Quantum Systems with Circular Symmetry
15.4 Questions and Problems
16 The Schrödinger Equation in Three Dimensions
16.1 Spherical Coordinates and Angular Momentum
16.2 Eigenfunctions of Angular Momentum
16.3 Diatomic Molecules
16.4 Spin and Angular Momentum
16.5 Addition of Angular Momentum
16.6 Free Particle in Spherical Coordinates
16.7 Questions and Problems
17 The Hydrogen Atom
17.1 Hydrogen Atom Wavefunctions and Energies
17.2 The Classical Limit of the Quantum Kepler Problem
17.3 Other "Hydrogenic" Atoms
17.4 Multielectron Atoms
17.5 Questions and Problems
18 Gravity and Electromagnetism in Quantum Mechanics
18.1 Classical Gravity and Quantum Mechanics
18.2 Electromagnetic Fields
18.3 Constant Electric Fields
18.4 Atoms in Electric Fields: The Stark Effect
18.5 Constant Magnetic Fields
18.6 Atoms in Magnetic Fields
18.7 Spins in Magnetic Fields
18.8 The Aharonov-Bohm Effect
18.9 Questions and Problems
19 Scattering in Three Dimensions
19.1 Classical Trajectories and Cross-Sections
19.2 Quantum Scattering
19.3 Electromagnetic Scattering
19.4 Partial Wave Expansions
19.5 Scattering of Particles
19.6 Questions and Problems
A: Dimensions and MKS-type Units for Mechanics, Electricity and Magnetism, and Thermal Physics
A.1 Problems
B: Physical Constants, Gaussian Integrals, and the Greek Alphabet
B.1 Physical Constants
B.2 The Greek Alphabet
B.3 Gaussian Probability Distribution
B.4 Problems
C: Complex Numbers and Functions
C.1 Problems
D: Integrals, Summations, and Calculus Results
D.1 Integrals
D.2 Summations and Series Expansions
D.3 Assorted Calculus Results
D.4 Real Integrals by Contour Integration
D.5 Plotting
D.6 Problems
E: Special Functions
E.1 Trigonometric and Exponential Functions
E.2 Airy Functions
E.3 Hermite Polynomials
E.4 Cylindrical Bessel Functions
E.5 Spherical Bessel Functions
E.6 Legendre Polynomials
E.7 Generalized Laguerre Polynomials
E.8 The Dirac d-Function
E.9 The Euler Gamma Function
E.10 Problems
F: Vectors, Matrices, and Group Theory
F.1 Vectors and Matrices
F.2 Group Theory
F.3 Problems
G: Hamiltonian Formulation of Classical Mechanics
G.1 Problems
REFERENCES
INDEX
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
Y
Z

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