# Eigenfunctions in Hilbert Space, Infinite Square Wells and Uncertainty

1. Mar 21, 2007

### neo2478

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.

2. Mar 21, 2007

### neo2478

Also can someone tell me why the code thingy for the formulas ain't working??

3. Mar 21, 2007

### vanesch

Staff Emeritus
Because the end tag of the tex part is [ / tex ] and not [ \ tex ]