Dummy indices in (products of) summations

In my quantum mechanics text book it states that if the normalisation
condition for a wave
packet Psi made of a superposition of states is

Psi*Psi=1

then the two occurences of Psi necessitate two different dummy indices in
the sum.
m amd n for example.

Is this a general thing in maths that if a function contains a sum then a
product of that function (with its complex conjugate in this case) requires
2 separate indices.
Regards
Zinc


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