1.introduction
2.the independent-electron approximation
2.1 starting hamiltonian
2.2 basis functions and basis sets
2.3 self-consistent field approximation
2.4 simplified scf calculational schemes
2.4.1 semi-empirical scf methods
2.4.2 pseudopotentials
2.5 koopmans'' theorem
2.6 homogeneous electron gas
2.7 local exchange potential - the xa method
2.8 shortcomings of the independent-electron approximation
2.9 unrestricted scf approximation
3.density functional theory
3.1 thomas-fermi method
3.2 hohenberg-kohn-sham theory
3.3 local-density approximation
3.4 results for atoms, molecules, and solids
3.5 extensions and limitations
4.quantum-chemical approach to electron correlations
4.1 configuration interactions
4.1.1 local and localized orbitals
4.1.2 selection of double substitutions
4.1.3 multireference ci
4.2 many-body perturbation theory
5.cumulants, partitioning, and projections
5.1 cumulant representation
5.1.1 ground-state energy
5.1.2 perturbation expansion
5.2 projection and partitioning techniques
5.2.1 coupled-electron-pair approximations
5.2.2 projections based on local operators
5.2.3 method of increments
5.3 coupled-cluster method
5.4 comparison with various trial wavefunctions
5.5 simplified correlation calculations
6.excited states
6.1 ci calculations and basis set requirements
6.2 excitation energies in terms of cumulants
6.3 green''s function method
6.3.1 perturbation expansions
6.3.2 the projection method
6.4 local operators
7.finite-temperature techniques
7.1 approximations for thermodynamic quantities
7.1.1 temperature green''s function
7.1.2 the projection method for t 4:0
7.2 functional-integral method
7.2.1 static approximation
7.3 monte carlo methods
7.3.1 sampling techniques
7.3.2 ground-state energy
8.correlations in atoms and molecules
8.1 atoms
8.2 hydrocarbon molecules
8.2.1 analytic expressions for correlation-energy
contributions
8.2.2 simplified correlation calculations
8.3 molecules consisting of first-row atoms
8.4 strength of correlations in different bonds
8.5 polymers
8.5.1 polyethylene
8.5.2 polyacetylene
8.6 photoionization spectra
9.semiconductors and insulators
9.1 ground-state correlations
9.1.1 semi-empirical correlation calculations
9.1.2 ab initio calculations
9.2 excited states
9.2.1 role of nonlocal exchange
9.2.2 the energy gap problem
9.2.3 hedin''s gw approximation
10.homogeneous metallic systems
10.1 fermi-liquid approach
10.2 charge screening and the random-phase approximation
10.3 spin fluctuations
11.transition metals
11.1 correlated ground state
11.2 excited states
11.3 finite temperatures
11.3.1 single-site approximation
11.3.2 two-sites approximation
11.3.3 beyond the static approximation
12.strongly correlated electrons
12.1 molecules
12.2 anderson hamiltonian
12.2.1 calculation of the ground-state energy
12.2.2 excited states
12.2.3 noncrossing approximation
12.3 effective exchange hamiltonian
12.3.1 schrieffer-wolff transformation
12.3.2 kondo divergency
12.3.3 fermi-liquid description
12.4 magnetic impurity in a lattice of strongly correlated
electrons
12.5 hubbard hamiltonian
12.5.1 ground-state: gutzwiller''s wavefunction and spin-density
wave state
12.5.2 excitation spectrum
12.5.3 the limits of one dimension and infinite dimensions
12.6 the t - j model
12.7 slave bosons in the mean-field approximation
12.8 kanamori''s t-matrix approach
13.heavy-fermion systems
13.1 the fermi surface and quasiparticle excitations
13.1.1 large versus small fermi surface
13.2 model hamiltonian and slave bosons
13.3 application of the noncrossing approximation
13.4 variational wavefunctions
13.5 quasiparticle interactions
13.6 quasiparticle-phonon interactions based on strong
correlations
14.superconductivity and the high-te materials
14.1 the superconducting state
14.1.1 pair states
14.1.2 bcs ground state
14.1.3 pair breaking
14.2 electronic properties of the high-tc materials
14.2.1 electronic excitations in the cu-o planes
14.2.2 calculation of the spectral weight by projection
techniques
14.2.3 size of the fermi surface
14.3 other properties of the cuprates
14.3.1 loss of antiferromagnetic order
14.3.2 optical conductivity
14.3.3 magnetic response
14.4 heavy fermions in nd2_xcexcuo4
appendix
a.relation between exc[p] and the pair distribution function
b.derivation of several relations involving cumulants
c.projection method of mori and zwanzig
d.cross:over from weak to strong correlations
e.derivation of a general form for ω）
f.hund''s rule correlations
g.cumulant representation of expectation values and correlation
functions
h.diagrammatic representation of certain expectation values
i.derivation of the quasiparticle equation
j.coherent-potential approximation
k.derivation of the nca equations
l.ground-state energy of a heisenberg antiferromagnet on a square
lattice
m.the lanczos method
references
subject index
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