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For my studies I have to read a part about approximation methods in Quantum Mechanics. Unfortunately I'm having difficulties understanding some concepts.

If I'm correct, for describing a multi fermionic system of n electrons, the Hartree Fock (HF) method uses a Slater determinant consisting of spin-orbitals to approximate the system wave function.

$$ \psi=(n!)^{-1/2} det|\phi_a(1) \phi_b(2) ...\phi_z(n)| $$

The Slater determinant is used to obey anti symmetry and thus the Pauli Exclusion Principle. Then the Hartree Fock equation is used to obtain the spin-orbitals. By means of a Self Consisting Field approach the spin-orbitals are then optimized until the wave functions do not change anymore. The HF ground state is then found by constructing a Slater Determinant of the n energetically lowest orbitals.

For the Configuration Interaction (CI) method the electronic wave function is constructed of a linear combination of several Slater determinants. These determinants correspond to different singly, doubly, triply, etc. excited states.

Does this mean that you do not take into account any excited states for constructing your electronic wave function using the Hartree Fock method and that you are only able to find the ground state wave function?

I really have a hard time understanding any of this so if you would be able to explain it simply it is much appreciated :)

Thanks in advance!

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# I Hartree Fock v.s. Configuration Interaction

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