Integration by parts of derivative of expectation value problem

[Normalization]

Homework Statement

I don't know how the writer of the book took integral of the first statement and got the second statement? Can anybody clarify on this?

Homework Equations

Given in the photo

The Attempt at a Solution

When I took the integral I just ended up with the exact same statement but without the negative sign behind the (ihbar/2m)

 

[tiny-tim]

Welcome to PF!

Hi Normalization! Welcome to PF!

When I took the integral I just ended up with the exact same statement but without the negative sign …

But that negative sign is always there in integration by parts.

(see the last equation in your photo)

 

[Normalization]

Oh w8 (facepalm) they haven't actually integrated yet? Wow... I feel so stupid right now. I thought they already integrated both products inside the brackets in which case -$\int$$\frac{\partial\Psi^*}{\partial\ x}$$\Psi$dx-$\int$$\frac{\partial\Psi}{\partial\ x}$×-$\Psi^*$dx Which would be the exact same thing. Alright thanks I guess...

 

[tiny-tim]

I'm not convinced you've got this.

They have integrated that big bracket, and so they also differentiate the x (to get 1) …

the […] term is 0 (so they haven't written it), and that only leaves the ∫ term, which always has a minus in front of it.

 

[Normalization]

I'm not convinced you've got this.

They have integrated that big bracket, and so they also differentiate the x (to get 1) …

the […] term is 0 (so they haven't written it), and that only leaves the ∫ term, which always has a minus in front of it.

Yes,yes,yes I know but I thought they had already taken the integral of -int(df/dx g dx)

 

[Normalization]

Which by nature should be equal to the left side of the equation. So it's fine I was just being daft