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The last part is this: find the expectation values of energy at t=0

The function that describes the particle of mass m is

A.SUM[(1/sqrt2)^n].[tex]\varphi[/tex]_n

where I've found A to be 1/sqrt2. The energy eigenstates are [tex]\varphi[/tex]_n with eigenvalue E_n=(n + 1/2)hw

I tried the usual expectation value way but I run into a horrible sum which seems to diverge I think. How shouldf I go about this??

Cheers guys!