Checking if Momentum Operator is Hermitian - Integration

  • Thread starter MPKU
  • Start date
  • #1
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Homework Statement



I'm checking to see if the momentum operator is Hermitian. Griffiths has the solution worked out, I'm just not following the integration by parts.

Homework Equations



int(u dv) = uv - int(v du)

The Attempt at a Solution



I've attached an image of my work.

It seems there should be an additional 'dx' with my 'v' term, but then the 'uv' portion would have a 'dx', which wouldn't make much sense to me.

Thanks for your time.
 

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Answers and Replies

  • #2
DrClaude
Mentor
7,556
3,894
If you set ##u = f^*##, then
$$
\frac{du}{dx} = \frac{df^*}{dx}
$$
hence
$$
du = \frac{df^*}{dx} dx
$$
 

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