Index change

Mar 2014
I do not understand why the indices of S, i.e. kl, change to pl, upon differentiation:

d/dcp* (cSc) = d/dcp* ("sum from k to N" "sum from l to N" ck*Sklcl) = "Sum from k to l" Splcl

Here, * indicates complex conjugation. Differentiating should leave Sc as this part is constant. I assume the summation over all k coefficients and wavefunctions disappears because c*, which is the differentiated variable, pairs with all wavefunctions of state k, and as it exits the expression upon differentiation, p is used instead to denote those wavefunctions whereas k now would be misleading. However, I do not think that the index p for the variable is chosen randomly.
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