Discover the Spin of an Electron Using Angular Momentum Operator and Eigenvalues

rubertoda
Messages
33
Reaction score
0
I should Use
the fact that in general the eigenvalues of the square of the angular momentum
operator is J(J + 1)h and show the spin of the electron.

I have J= L+S and J2 = L2+ S2

Homework Statement




But how could i find the spin of the electron
 
Physics news on Phys.org
Not really, J^2 = L^2 + S^2 +2 L.S. And post the whole text of your problem.
 
dextercioby said:
Not really, J^2 = L^2 + S^2 +2 L.S. And post the whole text of your problem.
Yes, i was sloppy. I meant that. But, I am asked to show the spin of the electron, by knowing that the eigenvalue of J2 is usually J(J+1)hbar...what do they mean?

sthg like solving for S in J^2 = L^2 + S^2 +2 L.S?
 
rubertoda said:
Yes, i was sloppy. I meant that. But, I am asked to show the spin of the electron, by knowing that the eigenvalue of J2 is usually J(J+1)hbar2...what do they mean?

sthg like solving for S in J^2 = L^2 + S^2 +2 L.S?

So how to do this
 
Can you, please, post the text of your problem, exactly as it appears in your book ?
 
Calculate the square of the total spin operator and find all its eigenvalues. Use
the fact that in general the eigenvalues of the square of the angular momentum
operator is J(J + 1)¯h
2
to find the spin of the electron.



the firts one i have fixed..
 

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

Why a particle with spin=0 can't posses a magnetic dipole moment?
Replies
17
Views
3K
Spin-Orbit Coupling in Hydrogen Atom: Understanding the Calculation
Replies
6
Views
3K
Spin-orbit coupling for positronium
Replies
1
Views
2K
Probability of the outcomes of ##J^2## and ##J_{z}##?
Replies
4
Views
2K
What happens to an atom's angular momentum when it absorbs an electron?
Replies
1
Views
2K
The time-dependence of the expectation values of spin operators
Replies
1
Views
2K
Is Total Angular Momentum J=L+s or J=L1+L2?
Replies
3
Views
2K
Consider the hypothetical decay of the Φ(1020) meson into 3 pions
Replies
4
Views
2K
I Addition of angular momenta
Replies
1
Views
496
How Do You Calculate Eigenvalues for Combined Spins in Quantum Mechanics?
Replies
14
Views
3K

Hot Threads

Recent Insights

Back
Top