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Answer:
answer :
This depends on the definition of the momentum operator. If it is defined as the infinitesimal generator of translations, then it is Hermitian by virtue of the fact that the translation operator is unitary. This derivation is the most enlightening, because it does not depend on writing down the form of the momentum operator with respect to a particular basis, and it holds for the infinitesimal generator of any smooth family of unitary operators connected to the identity
Since this is true for all ψ , we conclude that p=p† . Note that we have not used any properties of the translation operator other than unitarity (and the fact that we are taking the derivative at the identity).
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