Checking if Momentum Operator is Hermitian - Integration

  • Thread starter MPKU
  • Start date
  • #1
53
0

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.
 

Attachments

  • integral.jpg
    integral.jpg
    24.6 KB · Views: 414

Answers and Replies

  • #2
DrClaude
Mentor
7,754
4,254
If you set ##u = f^*##, then
$$
\frac{du}{dx} = \frac{df^*}{dx}
$$
hence
$$
du = \frac{df^*}{dx} dx
$$
 

Related Threads on Checking if Momentum Operator is Hermitian - Integration

Replies
7
Views
2K
  • Last Post
Replies
3
Views
11K
  • Last Post
Replies
1
Views
687
Replies
9
Views
2K
Replies
2
Views
1K
  • Last Post
Replies
10
Views
10K
Replies
13
Views
2K
Replies
7
Views
5K
Replies
8
Views
8K
Replies
2
Views
4K
Top