|
|
1 | (7) |
|
Schrodinger Theory from the Perspective of `Classical' Fields Derived from Quantal Sources |
|
|
7 | (42) |
|
Time-Dependent Schrodinger Theory |
|
|
7 | (1) |
|
Definitions of Quantal Sources |
|
|
8 | (4) |
|
|
9 | (1) |
|
Spinless Single--Particle Density Matrix γ(rr't) |
|
|
9 | (1) |
|
Pair--Correlation Density g(rr't), and Fermi--Coulomb Hole ρxc(rr't) |
|
|
10 | (1) |
|
|
11 | (1) |
|
Definitions of `Classical' Fields |
|
|
12 | (2) |
|
Electron--Interaction Field εee(rt) |
|
|
12 | (1) |
|
Differential Density Field D(rt) |
|
|
12 | (1) |
|
|
13 | (1) |
|
Current Density Field J(rt) |
|
|
13 | (1) |
|
Energy Components in Terms of Quantal Sources and Fields |
|
|
14 | (2) |
|
Electron-Interaction Potential Energy Eee(t) |
|
|
14 | (1) |
|
|
15 | (1) |
|
External Potential Energy Eext(t) |
|
|
16 | (1) |
|
Pure State Differential and Integral Virial Theorems |
|
|
16 | (2) |
|
The Quantum--Mechanical `Hydrodynamical' Equations |
|
|
18 | (1) |
|
The Internal Field of the Electrons and Ehrenfest's Theorem |
|
|
19 | (4) |
|
The Harmonic Potential Theorem |
|
|
23 | (1) |
|
Time-Independent Schrodinger Theory: Ground and Bound Excited States |
|
|
24 | (6) |
|
|
26 | (1) |
|
Asymptotic Structure of Wavefunction and Density |
|
|
27 | (3) |
|
Examples of the Field Perspective: The Ground and First Excited Singlet State of the Hooke's Atom |
|
|
30 | (13) |
|
Wavefunction, Orbital Function, and Density |
|
|
31 | (3) |
|
Fermi--Coulomb Hole Charge Distribution ρxc(rr') |
|
|
34 | (2) |
|
Hartree, Pauli--Coulomb, and Electron--Interaction Fields eH(r), Exc(r), Eee(r) and Energies EH, Exc, Eee |
|
|
36 | (3) |
|
Kinetic Field Z(r) and Kinetic Energy T |
|
|
39 | (1) |
|
Differential Density Field D(r) |
|
|
40 | (2) |
|
Total Energy E and Ionization Potential I |
|
|
42 | (1) |
|
Expectations of Other Single-Particle Operators |
|
|
42 | (1) |
|
Schrodinger Theory and Quantum Fluid Dynamics |
|
|
43 | (6) |
|
|
43 | (2) |
|
|
45 | (4) |
|
Quantal Density Functional Theory |
|
|
49 | (50) |
|
Time--Dependent Quantal Density Functional Theory |
|
|
50 | (13) |
|
|
51 | (3) |
|
|
54 | (3) |
|
Total Energy and Components in Terms of Quantal Sources and Fields |
|
|
57 | (3) |
|
Effective Field Feff(rt) and Electron-Interaction Potential Energy υee(rt) |
|
|
60 | (3) |
|
|
63 | (2) |
|
|
63 | (1) |
|
|
63 | (1) |
|
|
64 | (1) |
|
Time-Independent Quantal Density Functional Theory |
|
|
65 | (6) |
|
|
66 | (1) |
|
|
67 | (1) |
|
Total Energy and Components |
|
|
67 | (1) |
|
Effective Field Feff(r) and Electron-Interaction Potential Energy υee(r) |
|
|
68 | (1) |
|
|
69 | (1) |
|
Highest Occupied Eigenvalue εm |
|
|
70 | (1) |
|
|
70 | (1) |
|
Application of Q--DFT to the Ground and First Excited Singlet State of the Hooke's Atom |
|
|
71 | (15) |
|
S System Wavefunction, Spin--Orbitals, and Density |
|
|
71 | (1) |
|
Pair--Correlation Density; Fermi and Coulomb Hole Charge Distributions |
|
|
72 | (5) |
|
Hartree, Pauli, and Coulomb Fields εH(r), εx(r), εc(r) and Energies EH, Ex, Ec |
|
|
77 | (2) |
|
Hartree WH(r), Pauli Wx(r), and Coulomb Wc(r) Potential Energies |
|
|
79 | (2) |
|
Correlation-Kinetic Field Ztc(r), Energy Tc, and Potential Energy Wtc(r) |
|
|
81 | (4) |
|
Total Energy and Ionization Potential |
|
|
85 | (1) |
|
Quantal Density Functional Theory of Hartree Fock and Hartree Theories |
|
|
86 | (13) |
|
|
87 | (2) |
|
The Slater--Bardeen Interpretation of Hartree--Fock Theory |
|
|
89 | (1) |
|
Theorems in Hartree--Fock Theory |
|
|
90 | (1) |
|
Q--DFT of Hartree--Fock Theory |
|
|
91 | (3) |
|
|
94 | (2) |
|
|
96 | (3) |
|
The Hohenberg--Kohn Theorems and Kohn--Sham Density Functional Theory |
|
|
99 | (26) |
|
The Hohenberg--Kohn Theorems |
|
|
100 | (7) |
|
Inverse Maps and Constrained Search |
|
|
105 | (2) |
|
Kohn--Sham Density Functional Theory |
|
|
107 | (4) |
|
Time--Dependent Density Functional Theory |
|
|
111 | (3) |
|
Corollary to the Hohenberg--Kohn Theorem |
|
|
114 | (11) |
|
|
115 | (5) |
|
|
120 | (2) |
|
|
122 | (3) |
|
Physical Interpretation of Kohn--Sham Density Functional Theory |
|
|
125 | (28) |
|
Interpretation of the Kohn--Sham Electron--Interaction Energy Functional EeeKS[ ρ] and Its Derivative υee(r) |
|
|
126 | (4) |
|
Adiabatic Coupling Constant Scheme |
|
|
130 | (7) |
|
Q--DFT Within Adiabatic Coupling Constant Framework |
|
|
131 | (2) |
|
KS--DFT Within Adiabatic Coupling Constant Framework |
|
|
133 | (2) |
|
Q--DFT and KS--DFT in Terms of the Adiabatic Coupling Constant Perturbation Expansion |
|
|
135 | (2) |
|
Interpretation of the Kohn--Sham `Exchange' Energy Functional ExKS[ ρ] and Its Derivative υx(r) |
|
|
137 | (1) |
|
Interpretation of the Kohn--Sham `Correlation' Energy Functional EcKS[ ρ] and Its Derivative υc(r) |
|
|
138 | (1) |
|
Interpretation of the KS--DFT of Hartree--Fock Theory |
|
|
139 | (1) |
|
Interpretation of the KS--DFT of Hartree Theory |
|
|
140 | (1) |
|
The Optimized Potential Method |
|
|
141 | (5) |
|
The Exchange--Only Optimized Potential Method |
|
|
142 | (4) |
|
Physical Interpretation of the Optimized Potential Method |
|
|
146 | (7) |
|
Interpretation of `Exchange--Only' OPM |
|
|
147 | (6) |
|
Quantal Density Functional Theory of the Density Amplitude |
|
|
153 | (14) |
|
Density Functional Theory of the B System |
|
|
154 | (4) |
|
DFT Definitions of the Pauli Kinetic and Potential Energies |
|
|
157 | (1) |
|
Derivation of the Differential Equation for the Density Amplitude from the Schrodinger Equation |
|
|
158 | (3) |
|
Quantal Density Functional Theory of the B System |
|
|
161 | (5) |
|
Q--DFT Definitions of the Pauli Kinetic and Potential Energy |
|
|
164 | (2) |
|
|
166 | (1) |
|
Quantal Density Functional Theory of the Discontinuity in the Electron--Interaction Potential Energy |
|
|
167 | (20) |
|
Origin of the Discontinuity of the Electron--Interaction Potential Energy |
|
|
168 | (3) |
|
Expression for Discontinuity Δ in Terms of S System Eigenvalues |
|
|
171 | (3) |
|
Correlations Contributing to the Discontinuity According to Kohn--Sham Theory |
|
|
174 | (1) |
|
Quantal Density Functional Theory of the Discontinuity |
|
|
175 | (11) |
|
Correlations Contributing to the Discontinuity According to Q-DFT: Analytical Proof |
|
|
177 | (3) |
|
|
180 | (6) |
|
|
186 | (1) |
|
Further Insights Derived Via Quantal Density Functional Theory |
|
|
187 | (28) |
|
The Local Density Approximation in Kohn--Sham Theory |
|
|
189 | (16) |
|
Derivation and Interpretation of Electron Correlations Via Kohn--Sham Theory |
|
|
189 | (3) |
|
Derivation and Interpretation of Electron Correlations Via Quantal Density Functional Theory |
|
|
192 | (6) |
|
Structure of the Fermi Hole in the Local Density Approximation |
|
|
198 | (5) |
|
|
203 | (2) |
|
|
205 | (10) |
|
Derivation of the Exact `Slater Potential' |
|
|
205 | (3) |
|
Why the `Slater Exchange Potential' Does Not Represent the Potential Energy of an Electron |
|
|
208 | (2) |
|
Correctly Accounting for the Dynamic Nature of the Fermi Hole |
|
|
210 | (2) |
|
The Local Density Approximation in Slater Theory |
|
|
212 | (3) |
|
|
215 | (6) |
|
Asymptotic Structure of the Electron-Interaction Potential Energy in the Classically Forbidden Region of Atoms and Metal Surfaces |
|
|
216 | (5) |
|
Asymptotic Structure in Atoms |
|
|
216 | (1) |
|
Asymptotic Structure at Metal Surfaces |
|
|
217 | (4) |
|
|
221 | (24) |
|
A.Proof of the Pure State Differential Virial Theorem |
|
|
221 | (4) |
|
B. Proof of the Harmonic Potential Theorem |
|
|
225 | (2) |
|
C. Analytical Expressions for the Properties of the Ground and First Excited Singlet States of the Hooke's Atom |
|
|
227 | (9) |
|
C.1 Ground State (k = 1/4) |
|
|
227 | (5) |
|
C.2 First Excited Singlet State (k = 0.144498; w = √k = 0.381029) |
|
|
232 | (4) |
|
D. Derivation of the Kinetic--Energy--Density Tensor for Hooke's Atom in Its Ground State |
|
|
236 | (2) |
|
E. Proof of the S System Differential Virial Theorem |
|
|
238 | (2) |
|
F. Derivation of the Pair--Correlation Density in the Local Density Approximation for Exchange |
|
|
240 | (5) |
References |
|
245 | (8) |
Index |
|
253 | |