How Does the Expectation Value Simplify to iCm/(pi*hbar)^1/2?

[Skullmonkee]

Just a quick question.
I finished an expectation value sum and noticed that the given solution had me stumped.
Ive attached a quick picture of the simplifying process which was given as the solution.

The only thing i don't understand is how to get the value iCm/(pi*hbar)^1/2.
I don't know how it simplifies to that as i get another answer. You'll have to have a look at the attached picture to see what i mean.
Any help would be appreciated.
Thanks.

 

[CompuChip]

The first factor underlined in red comes from the two factors of
$$\left( \frac{\sqrt{C m}}{\pi \hbar} \right)^{1/4}$$
on the top line, which are - IIRC - from the normalisation of your wave function.
The second factor in red comes from the $-i\hbar$ in front of the d/dx, combined with the $2 \left( \sqrt{C m}/(2 \hbar) \right)$ which comes down from the exponential when you apply the d/dx.

In the third red underlined term, I suspect that instead of C m there should be (C m)^(3/4). Because if you let k = sqrt(C m) you have a sqrt(k) multiplied by k, which gives k^(3/2), i.e. ((C m)^(1/2))^(3/2) = (C m)^(3/4).

 

[Skullmonkee]

Thanks CompuChip

That was my thought exactly. I could not see how there was not a (C m)^(3/4) term. At least i was on the ball there. I suppose that the solution which was given (the working i showed in the pic) is just wrong then?

 

[Avodyne]

The mistake is at the beginning. The 1/4 should be 1/2 for correct normalization.