fm JWBS043-Rogers October 8, 2010 21:3 Printer Name: Yet to Come
CONTENTS xv16 Wave Mechanics of Simple Systems 248
16.1 Wave Motion, 248
Figure 16.1 Graph of sin(x),sin(2x), and sin(3x)Shown
over the Interval 0 ,π., 249
16.2 Wave equations, 249
Eigenvalues and Eigenvectors, 250
16.3 The Schrodinger Equation, 250 ̈
16.4 Quantum Mechanical Systems, 251
is a Vector, 251
The EigenfunctionPostulate, 252
16.5 The Particle in a One-Dimensional Box, 253
Figure 16.2 Wave Forms for the First Three Wave
Functions of the Particle in a Box., 254
Fundamentals and Overtones, 254
Figure 16.3 A Mathcad©CSketch of the Born Probability
Densities at the First Three Levels of the Particle in
a Box., 255
16.6 The Particle in a Cubic Box, 255
Separable Equations, 256
16.6.1 Orbitals, 257
Figure 16.4 The Ground State Orbital of a
Particle Confined to a Cubic Box., 257
16.6.2 Degeneracy, 257
Figure 16.5 The First Excited State of a Particle
Confined to a Cubic Box., 257
16.6.3 Normalization, 257
Figure 16.6 The Degenerate Energy Levels for
the Hydrogen Atom., 258
16.7 The Hydrogen Atom, 258
The Radial Equation and Probability “Shells”, 258
16.8 Breaking Degeneracy, 259
Figure 16.7 Reduced Degeneracy in Energy Levels for
Hydrogen-Like Atoms., 260
16.8.1 Higher Exact Solutions for the Hydrogen Atom, 260
Table 16.1 The First Six Wave Functions for Hydrogen., 261
Table 16.2 The First Three s Wave Functions for
Hydrogen(Simplified Form)., 261
Figure 16.8 Roots of the Radial 3s Wave Function of
Atomic Hydrogen as a Function of Distance r ., 261
Figure 16.9 The Radial Probability Density for
an Electron in the 3s Orbital of Hydrogen., 262
16.9 Orthogonality and Overlap, 262
Figure 16.10 The Radial Node of the 2 p Atomic
Orbital., 262