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Hermitian Conjugate of

We wish to compute the Hermitian conjugate of the operator
.
We will use the integral to derive the result.

We can integrate this by parts, differentiating the
and integrating to get
.

So the Hermitian conjugate of
is
.
Note that the Hermitian conjugate of the momentum operator is
which is the same as the original operator.
So the momentum operator is Hermitian.

Jim Branson
2013-04-22