Show that Momentum Operator is Hermitian: Q&A

[krootox217]

Homework Statement

Hi, my task is to show that the momentum operator is hermitian.

I found a link, which shows how to solve the problem:

http://www.colby.edu/chemistry/PChem/notes/MomentumHermitian.pdf

But there are two steps that I don't understand:

1. Why does the wave function approach zero for long distances (for a confined particle)? Can someone explain me this?

2. I don't understand the last step. I got

And now i don't know how to use the last equation on the paper to show that it is the same.

Can someone help me?

Homework Equations

See above

The Attempt at a Solution

See above[/B]

 

[vela]

Do you know the definition of hermitian?

 

[krootox217]

I know what a hermitian matrix is. But here I'm not sure. I guess that the operator is the same as the complex conjugate of the operator?

 

[vela]

You should start there then. There's no need to guess. The definition should be explained on your textbook or notes. You want to figure out specifically what it means when you say an operator is the same as its complex conjugate. It's probably explained in terms of inner products.