Hamiltonian in c-operator form

2 Hamiltonian in c-operator form For a free-electron, the Schrodinger equation takes the form  

Now (4.19) has solutions for an infinite number of energies Eu u = whose corresponding state functions u), which satisfy 1,2.), 

It is convenient to choose u), so that Tuv has only diagonal elements. One such choice is the plane-wave e k r, for which (4.20) and (4.21) yield (Taylor 1970) 

A similar derivation for the potential energy operator V leads to the result 

Turning to the situation where the electrons interact, requires we add to (4.28) a 2-electron repulsion term 

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See also in sourсe #XX -- [ ]

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