- #1

- 8

- 0

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.