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 'Please tell me where I am going wrong in this integral'

##|\Psi|^2=\frac{1}{\sqrt{\pi b^2}}\exp(\frac{-(x-x_0)^2}{b^2}).## ##\braket{x}=\frac{1}{\sqrt{\pi b^2}}\int_{-\infty}^{\infty}dx\,x\exp(-\frac{(x-x_0)^2}{b^2}).## ##y=x-x_0 \quad x=y+x_0 \quad dy=dx.## The boundaries remain infinite, I believe. ##\frac{1}{\sqrt{\pi b^2}}\int_{-\infty}^{\infty}dy(y+x_0)\exp(\frac{-y^2}{b^2}).## ##\frac{2}{\sqrt{\pi b^2}}\int_0^{\infty}dy\,y\exp(\frac{-y^2}{b^2})+\frac{2x_0}{\sqrt{\pi b^2}}\int_0^{\infty}dy\,\exp(-\frac{y^2}{b^2}).## I then resolved the two...
View full post »

Thread 'Direction of the magnetic field of an oscillating charge'

Hello everyone, I’m considering a point charge q that oscillates harmonically about the origin along the z-axis, e.g. $$z_{q}(t)= A\sin(wt)$$ In a strongly simplified / quasi-instantaneous approximation I ignore retardation and take the electric field at the position ##r=(x,y,z)## simply to be the “Coulomb field at the charge’s instantaneous position”: $$E(r,t)=\frac{q}{4\pi\varepsilon_{0}}\frac{r-r_{q}(t)}{||r-r_{q}(t)||^{3}}$$ with $$r_{q}(t)=(0,0,z_{q}(t))$$ (I’m aware this isn’t...
View full post »

Thread 'Initial conditions for orbits around a wormhole'

Hi, I had an exam and I completely messed up a problem. Especially one part which was necessary for the rest of the problem. Basically, I have a wormhole metric: $$(ds)^2 = -(dt)^2 + (dr)^2 + (r^2 + b^2)( (d\theta)^2 + sin^2 \theta (d\phi)^2 )$$ Where ##b=1## with an orbit only in the equatorial plane. We also know from the question that the orbit must satisfy this relationship: $$\varepsilon = \frac{1}{2} (\frac{dr}{d\tau})^2 + V_{eff}(r)$$ Ultimately, I was tasked to find the initial...
View full post »

Similar threads

Expectation Values <E> and <E^2>
Replies
6
Views
4K
Confusion In Writing Identical Particle Wavefunctions
Replies
12
Views
314
Normalisation of the radial wavefunction in 2s state?
Replies
1
Views
4K
B A stupidly basic question about expectation value
Replies
8
Views
2K
The expectation value for the radial part of the wavefunction of Hydrogen.
Replies
2
Views
4K
The time-dependence of the expectation values of spin operators
Replies
1
Views
2K
Expectation Value of Position for Even Wavefunction
Replies
3
Views
4K
Hydrogen Atom: Wavefunction collapse after measurement of Lz
Replies
20
Views
3K
Finding meaning in the Phase of the wavefunction
Replies
11
Views
1K
Darwin term in a hydrogen atom - evaluating expectation values
Replies
1
Views
3K

Hot Threads

Recent Insights

Back
Top