Recent content by Gunthi

Yes but my question is how do these operators act on these states? The basis I'm using only shows the m numbers of two particles because I've already summed the spins of the first two...

Homework Statement Find the energies for a 3 spin-1/2 particles with the Hamiltonean: H=\frac{E_0}{\hbar^2}(\vec{S_1}.\vec{S_3}+\vec{S_2}.\vec{S_3}) The Attempt at a Solution From the Clebsh-Gordon table one gets all the spin functions...

I'm just posting this so that the thread doesn't seem closed.

Thanks for the book! I tried to see if there was anything in Landau that could help but didn't find it yet. Anyhow, I found this http://solar.physics.montana.edu/dana/ph411/p_brack.pdf and I can't figure out why, in page 2 after equation (3) \frac{\partial q_1}{\partial t}=0. Isn't q_1 also a...

I've been messing around with the coordinates and got this: If we have a general invertible transformation of the type Q=Q(q,p,t)\Leftrightarrow q=q(Q,P,t) and P=P(q,p,t)\Leftrightarrow p=p(P,Q,t) then the following is true: \begin{matrix} \dot{q}=\frac{\partial q}{\partial...

I have another question related to this problem. Does having the generating function guarantee that the coordinate transformation associated with it is canonical? Or is it a necessary but not sufficient condition?

Homework Statement Given the transformation Q=qe^{\gamma t} and P=pe^{-\gamma t} with the Hamiltonean H=\frac{p^2e^{-2\gamma t}}{2m}+\frac{m\omega^2q^2e^{2\gamma t}}{2} show that the transformation is Canonical Homework Equations I know that the condition for a transformation to be...

Hi tiny-tim! :smile: I would also have to switch the 2nd and 3rd columns right? Then I would just calculate the eigenvalues of the 2x2 matrices separately? I've been searching for properties of block matrices that could justify this, but to no avail. Is there a theorem that demonstrates...

Homework Statement Find the allowed energies for a spin-3/2 particle with the given Hamiltonian: \hat{H}=\frac{\epsilon_0}{\hbar}(\hat{S_x^2}-\hat{S_y^2})-\frac{\epsilon_0}{\hbar}\hat{S_z} The Attempt at a Solution The final matrix I get is: \begin{pmatrix} \frac{3}{2} & 0 &...

Got it! Thanks!

Hi there, I'm trying to figure out how the sum of three cosines exposed in page 2 of: http://www.mrl.ucsb.edu/~seshadri/2004_100A/100A_MillerBragg.pdf can be proved... Any help would be appreciated... Thanks in advance, G.

So the covariant derivative is distributive like the Lie derivative? How could I prove that? Thanks

\nabla_a[(-g)^{\frac{1}{2}}T^a] = T^a\nabla_a[(-g)^{\frac{1}{2}}]+(-g)^{\frac{1}{2}}\nabla_aT^a I just realized that I don't quite understand how a tensor density behaves when multiplied by a vector. I'm trying to find some clues in D'Inverno's book but I'm getting more confused. Thanks in...

Aren't tensors non-commutative? If so you couldn't 'shuffle' the x's as you say right? I'm trying to solve this exercise but I get a little confused in what one is allowed or not to do with dummy indices... I can't seem to get the indices in the right order because if I change an 'a' with a...

Got it. Thanks ;)