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Derive the Fock Equations — Calculus of variations — where the 2 comes from

Exercises

Quantum Chemistry I › Unit 7 · The Fock problem › Derive the Fock Equations › all problems

Practice Problem 2 of 9

Calculus of variations — where the 2 comes from

Problem
Show that the first-order change of under (real orbitals) is . Where does the 2 come from?

Solution

Predict before reading on. This is the first collection step of the worked example, isolated. Which two terms of the expansion survive at first order?

For a Hermitian operator and real functions the two cross terms are equal — hence the 2. Every “2” in the derivation has this same pedigree.