ABSTRACT
In the last chapter, we showed that the Hamiltonian for interacting electrons in a solid can be written in second-quantized form as https://www.w3.org/1998/Math/MathML"> H ^ e = Σ v λ 〈 v | h ^ ( 1 ) | λ 〉 a v † a λ + 1 2 Σ v λ α β 〈 v λ | e 2 | r 1 − r 2 | | α β 〉 a v † a λ † a β a α , ( 4.1 ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429037245/cc3a6600-aaec-4350-ba37-6c8d1f17d018/content/math95.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> where https://www.w3.org/1998/Math/MathML"> h ˆ ( 1 ) = p ˆ 1 2 / 2 m + V ˆ i o n ( r 1 ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429037245/cc3a6600-aaec-4350-ba37-6c8d1f17d018/content/inline-math65.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> and the Greek letters denote single-particle orbitals. In this chapter, we introduce the Hartree-Fock approximation to the correlated-electron problem. The basic assumption of this approximation is that the ground state is the same as that of the noninteracting system. The energy is taken to be the expectation value in this state.
