So, how do you know if they are in S=0 state or S=1 state? Is this where isospin comes in (Griffiths mentioned this, but I didn't know what he was talking about)?
This is from Griffiths "Introduction to elementary particles", chapter 5: bound states. pp 180 - 184.
the spins of the quarks (u,d,s) are all 1/2, so \left(S_u + S_d \right)^2 should aways be 2\hbar, but in the text it says it is equal to 0 for \Lambda (it says it is equal to 2\hbar for...
Thanks for the reply.
When you say for S=1 or S=0, what does that correspond to? I thought it was just an isospin of the particle (so 1/2 for \Xi and 0 for \Lambda), but I guess that's not the case. In the text (Griffiths), he says something about spins being "parallel" in the decuplet case...
Homework Statement
I am trying to derive the mass of \Xi using the formula:
M\left(baryon\right)=m_1 + m_2 + m_3 + A' \left[\frac{S_1 \cdot S_2}{m_1 m_2} +\frac{S_1 \cdot S_3}{m_1 m_3} + \frac{S_2 \cdot S_3}{m_2 m_2\3}\right]
Homework Equations
We have:
S_1 \cdot S_2 + S_1 \cdot S_3 +...
I got to the right answer by substituting:
E = \left|p_3\right| +\left(\left|p_1\right|^2 + \left|p_3\right|^2 - 2\left|p_1\right|\left|p_3\right| cos\theta\right)^{1/2}
Then:
dE = \frac{E-\left|p_1\right| cos\theta}{E-\left|p_3\right|}d\left|p_3\right|
Then using definition of the...
r = (x, y, z) and p = (px, py, pz).
I assume you know how to take a cross product. The only other thing is that p = -i\hbarh\del which acts on the wavefunction \Psi, and you can't exchange r and p (ie. rxp is not the same as pxr)
I hope that helps
Hm... Did I not follow the PF guideline correctly, or is this too long (and/or boring) of a question?
It's frustrating because it seems like I'm only a couple of steps from getting the correct answer, so please help me out if you can. Thanks!
You should know from your class that the commutator [x, y] = xy - yx
you can express the L operator in terms of the coordinates x,y,z and the momentum operator p. Apply the commutator to a wavefunction psi and simplify!
Hope that gave you a clue.
Homework Statement
I am pretty sure it's been done many times before, but I can't seem to figure it out:
Consider the collision 1 + 2 -> 3 + 4 in the lab frame (2 at rest), with particles 3 and 4 massless. Derive the forumla for the differential cross section
Homework Equations
We have...
Yeah, I asked the prof, and it is a typo... I really don't like it when there is a typo in an assignment.
It was supposed to be B^{0} and \bar{B^{0}} as a decay process of Z^{0}.
Thanks for the help anyway!
-Rick
I will put the question in exact wording that the prof gave us:
Homework Statement
A B+ - B- pair is produced in the decay of at Z0. The B then decays to D + X, where X represents some other particles, with a lifetime of 1.638 x 10^12 s. On average how far will the B0 travel before...
Question:
If \hat{A} and \hat{B} are two operators such that \left[\hat{A},\hat{B}\right] = \lambda, where \lambda is a complex number, and if \mu is a second complex number, prove that:
e^{\mu\left(\hat{A}+\hat{B}\right)}=e^{\mu\hat{A}}e^{\mu\hat{B}}e^{-\mu^{2}\frac{\lambda}{2}}
What I...
Question:
Consider n+1 mutually independent random variables x+i from a normal distribution N(\mu ,\sigma ^{2}). Define:
\bar{x} = \frac{1}{n} \sum_{i=1}^{n}{x_{i}} and s^{2}=\frac{1}{n}\sum_{i=1}^{n}{\left(x_{i} - \bar{x}\right)^{2}}
Find the constant c so that the statistic
t=...
Question:
Consider the motion of a particle of mass m in a 1D potential V(x) = \lambda \delta (x). For \lambda > 0 (repulsive potential), obtain the reflection R and transmission T coefficients.
[Hint] Integrate the Schordinger equation from -\eta to \eta i.e.
\Psi^{'}(x=\epsilon...
If E < V, you will get a tunelling effect (one of those things I will have to learn myself), but I think basically when you come out from the other end of the barrier, the energy of the wave is lower than the original wave. I'm not sure what the wave function \Psi will look like though...