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Eschrig H. — The Fundamentals of Density Functional Theory
Eschrig H. — The Fundamentals of Density Functional Theory

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Название: The Fundamentals of Density Functional Theory

Автор: Eschrig H.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1996

Количество страниц: 205

Добавлена в каталог: 24.02.2007

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$L^p$-spaces      62
$X_{\alpha}$-approach      83
$\mathcal{L}(X, Y)$      118
$\sigma$-additive      112
Absolutely summable      113
action      164 167 168
Adiabatic approximation      56
Adiabatic forces      55
Adiabaticity assumption      52
Affine-linear      75 100
Almost everywhere (a.e.)      62 113
Angular momentum density      186
Anticommutator      31
Aufbau principle      90
Banach space      110
Banach space, reflexive      119
Banach — Alaoglu theorem      119
Base of topology      107
Bispinor      173
Bohr radius      17
Bolzano — Weierstrass theorem      108
Borel set      111
Bose condensed field      172
Bound minimum      124
Bounded linear functional      118
Bounded linear operator      117
Canonical momentum density      166
Cauchy net      110
Cauchy sequence      110
Chain rule for functional derivatives      123
Charge conservation      161
chemical potential      68 93
Classical electron radius      168
Closed set      106
Closed-shell Hartree — Fock method      25
Commutator      30
Compact      108
Complete set      29
Complete set, of spin-orbitals      15
Complete set, of TV-particle states      23
Complete space      110
Compton wavelength      169
Conjugate function      102
Conjugate functional      120
continuous      110
Continuous linear operator      118
Convex      101 120
Convex hull      105 121
Coupling constant      16 51
Creation and annihilation operators      32
Creation and annihilation operators, bosonic      30
Creation and annihilation operators, fermionic      31
Current density functional F[J, Q]      181
Current density functional H[J]      182
Current density functional K[J]      183
Current density, paramagnetic      189
de Rham’s cohomology      164
Density functional by Hohenberg and Kohn      77
Density functional by Hohenberg and Kohn, of kinetic energy      79
Density functional by Levy and Lieb      84
Density functional by Lieb      129
Density functional for N-particle density matrices      88
Density functional H[n]      138
Density functional K[n]      140
Density matrix      86
Density matrix, reduced      35—47
Density operator      32 40
Density parameter $r_s$      69
Dirac equation      172—174
Dirac operator      191
Dirac operator, squared      192
Dirac sea      191
Distance      108
Dual pair      120 121
d’Alembert operator      162
electromagnetic field      161
Electromagnetic potentials      161
Electron affinity      93
Electron liquid, homogeneous      68 144—148
Electronegativity      94
Ensemble state      86
Essential supremum (ess sup)      62
Exchange and correlation energy      47 149 189
Exchange and correlation field      187
Exchange and correlation hole      47—50
Exchange energy      26
Exchange energy, of the homogeneous electron liquid      146
Exchange hole      40 48
Exchange potential operator      27
Exchange term      20
F-derivative      122
Fenchel’s duality      126
Fermi energy      68
Fermi radius      23
Fermion gas, interaction-free      38
Fermion gas, interaction-free, homogeneous      22 37 40 48
Field operators      32
Fine structure constant      160 169
Finite from below      101
Fock operator      27 28
Fock space      29
Four-current density      163 173 183
Four-field tensor      163
Four-momentum      167
Four-potential      163
Four-velocity      167
Fractional orbital occupation numbers      86
Free Dirac field      174
Free minimum      124
Free photon field      170
Functional derivative      81 122—124
Fundamental form      162
Fundamental tensor      162
G-derivative      122
Gap correction      152
Gauge invariance      76 181 184
Generalized sequence      108
Gradient expansion      73
Groundstate      75
Groundstate energy      75 128 181
Groundstate energy, ensemble      86
Groundstate, degenerate      78
Groundstate, determinantal      79
Groundstate, ensemble      86
Groundstate, non-degenerate      78
Groundstate, of the quantum field      179
Groundstate, spin-polarized      95
Hahn — Banach theorem      103 121
Hamiltonian      13
Hamiltonian density      166
Hamiltonian density, of electromagnetic coupling      175
Hamiltonian, effective, of the inhomogeneous quantum field system      180
Hamiltonian, field quantized      33
Hamiltonian, for Coulomb systems      54
Hamiltonian, for Coulomb systems, total      55
Hamiltonian, in Heisenberg representation      24
Hamiltonian, in momentum representation      19
Hamiltonian, in natural units      17
Hamiltonian, in occupation number representation      32
Hamiltonian, in Schrodinger representation      16
Hamiltonian, of QED      177
Hamiltonian, of the free Dirac field      175
Hamiltonian, of the free photon field      171
Hamiltonian, of the homogeneous electron liquid      144
Hamiltonian, on the torus      57
Hard potential barrier      76
Hartree energy      26 47
Hartree potential      27
Hartree unit      17
Hartree — Fock energy      26 28
Hartree — Fock orbitals      27
Hartree-Fock equations      27
Hausdorff property      106
Heisenberg picture      170
Heitler — London ansatz      50
Hellmann — Feynman theorem      52
Hilbert space      13 116
Hilbert space, N-particle, bosonic      16
Hilbert space, N-particle, fermionic      15
Hohenberg — Kohn variational principle      77 183
Holder’s Inequality      115
Hole state      33
Homo      28 94
Hyperplane      119
Hyperplane of support      121
Inf-sup problem      125
Inner point      106
Ionization potential      94
Janak’s theorem      89 93
Jump of the Kohn — Sham potential      141
kinetic energy      43 47
Kinetic energy functional      61
Kinetic energy, exchange and correlation contribution      52
Klein — Gordon equation      172
Kohn — Sham exchange and correlation energy      52
Kohn — Sham exchange and correlation hole      53 150
Kohn — Sham exchange and correlation potential      81 149 184
Kohn — Sham orbital      82
Kohn — Sham orbital energy      95 98
Kohn — Sham — Dirac equation      188
Kohn — Sham — Dirac equation, general      184 187
Koopmans’ theorem      28
Lagrange density      165
Lagrange function      126
Lagrange multiplier      124—126
Lagrange multiplier, abstract      126
Lebesgue integral      113
Lebesgue measure      111
Lebesgue space $L^p$      115—117
Legendre transform      102 120
Limes      106
Limes, of a net      108
Local current density approximation      189
Local density approximation (LDA)      83 148—152
Locally convex space      109
Lorentz gauge      162 171
Lorentz transformation      164
Lower semicontinuous      101 120
LUMO      28 93
Magnetization density      186
Main theorem for extremal problems      119
Maxwell’s equations      161 163
mean field      27
Measurable function      112
Measurable set      112
Metric space      108
Minimum problem      119
Minkowski’s geometry      162
Minkowski’s inequality      115
Molecular field      27 28
N-representable density      84
n-representable potential      77
Natural orbitals      88
Natural units      17
Neighbourhood      106
Net      108
Norm      109
Normal order      171 178
Open set      106
Open-shell Hartree — Fock method      25
Orbital current density      185
Orbital relaxation energy      28
p-summable function      114
Pair correlation function      40
Pair density      38
Particle density      23 35
Particle number operator      30
Pauli — Hellmann — Feynman theorem      52
Perdew — Zunger interpolation of $\varepsilon_{XC}$      148
Periodic boundary conditions      18
Poisson’s equation      65
Potential gauge constant      76
Pure state      35
Pure-state v-representable density      77
Quantum electrodynamics (QED)      160
Regular measure      112
Relativistic dispersion relation      167
Relativistic effects magnitude      160
Renormalization      34 171 179 183
Rest mass      167
Riesz — Fisher theorem      116
Saddle point      126
Scaled nuclear charges      54
Schrodinger picture      170
Schwarz’ inequality      116
Self-consistent field      28
Self-interaction      26 46 50 183 184
Seminorm      109
Side condition      124
simplex      87
Slater determinant      15
Sobolev’s inequality      129
Spin current density      186
Spin density      43
Spin magnetization density      43
Spin operator      14
Spin polarization      95—98
Spin polarization, degree of      44 146
Spin-density matrix      36 44
Spin-orbital      15
Spinor      14
Subdifferential      103 121
Subgradient      102 120
Tangent of support      103
Taylor expansion of a functional      123
Teller’s no-binding theorem      71
Thermodynamic limit      33 56—59 93
Thomas — Fermi energy      63
Thomas — Fermi energy, of the atom      67
Thomas — Fermi equation      64 153
Thomas — Fermi functional      61
Thomas — Fermi screening length      69
Thomas — Fermi — $\lambda$Weizsacker theory      73
Thomas — Fermi — Dirac theory      72
Topological space      106
topology      106
Torus      18 56 130 131
Total charge      179
Trace      36
Transition state      94
Vacuum permeability po      161
Vacuum permittivity eo      161
Virial theorem      55
Virial theorem, of Thomas — Fermi theory      71
von Barth — Hedin interpolation function $f(\zeta)$      147
Vorticity      189
Wavenumber space      18
Weak lower semicontinuous      120
Weak topology      119
Weak* topology      119
Young’s inequality      102
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