Eigenfunctions in Hilbert Space, Infinite Square Wells and Uncertainty

  • Thread starter neo2478
  • Start date
  • #1
8
0

Main Question or Discussion Point

Hi I'm kinda stuck with a couple quantum HW questions and I was wondering if you guys could help.

First, Is the ground state of the infinite square well an eigenfunction of momentum?? If so, why. If not, why not??

Second, Prove the uncertainty principle, relating the uncertainty in position (A=x) to the uncertainty in energy ([tex]B=p^2/(2m + V)[\tex]):

[tex]\sigma x\sigma H \geq \hbar/2m |<P>|[\tex]

For stationary states this doesn't tell you much -- why not??

And finally, Show that two noncommuting operators cannot have a complete set of common eigenfunctions. Hint: Show that if P(operator) and Q(operator) have a complete set of common eigenfunctions, the [P(operator),Q(operator)]f = 0 for any function in Hilbert space.

thanks in advance, Rob.
 

Answers and Replies

  • #2
8
0
Also can someone tell me why the code thingy for the formulas ain't working??
 
  • #3
vanesch
Staff Emeritus
Science Advisor
Gold Member
5,028
16
Also can someone tell me why the code thingy for the formulas ain't working??
Because the end tag of the tex part is [ / tex ] and not [ \ tex ]
 

Related Threads on Eigenfunctions in Hilbert Space, Infinite Square Wells and Uncertainty

Replies
10
Views
6K
Replies
4
Views
632
Replies
5
Views
3K
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
4
Views
3K
  • Last Post
Replies
6
Views
1K
  • Last Post
Replies
4
Views
1K
  • Last Post
Replies
20
Views
9K
Top