Can someone help me with expectation values for the radial wavefunction?

cwhitis
Messages
3
Reaction score
0
Show that the expectation value of Lz is -2h for the radial wavefunction Y2,-2. ? Can someone do this?
 
Physics news on Phys.org
Use the matrix representation for the basis l=2.

Remember that
<br /> \mathbf{L_z} = m\hbar<br />
 
Last edited:
Thanks but I still don't understand, could you work it out?
 
That's not how it works here. It's against the forum rules to provide solutions, and you need to show some attempt at solving the problem before you'll get help here.
 
The wavefunction is normalized. Radial function cannot be Y, that's the spherical harmonics. Just apply the expected value in the ket-bra notation
 
Thread 'Need help understanding this figure on energy levels'
This figure is from "Introduction to Quantum Mechanics" by Griffiths (3rd edition). It is available to download. It is from page 142. I am hoping the usual people on this site will give me a hand understanding what is going on in the figure. After the equation (4.50) it says "It is customary to introduce the principal quantum number, ##n##, which simply orders the allowed energies, starting with 1 for the ground state. (see the figure)" I still don't understand the figure :( Here is...
Thread 'Understanding how to "tack on" the time wiggle factor'
The last problem I posted on QM made it into advanced homework help, that is why I am putting it here. I am sorry for any hassle imposed on the moderators by myself. Part (a) is quite easy. We get $$\sigma_1 = 2\lambda, \mathbf{v}_1 = \begin{pmatrix} 0 \\ 0 \\ 1 \end{pmatrix} \sigma_2 = \lambda, \mathbf{v}_2 = \begin{pmatrix} 1/\sqrt{2} \\ 1/\sqrt{2} \\ 0 \end{pmatrix} \sigma_3 = -\lambda, \mathbf{v}_3 = \begin{pmatrix} 1/\sqrt{2} \\ -1/\sqrt{2} \\ 0 \end{pmatrix} $$ There are two ways...
Back
Top