Hello, I am finishing a computational project, one that is using monte carlo to simulate a lennard-jones fluid.
Very straightforward project - the only twist is one that asks to come up with an algorithm/method that moves all particles at once, rather than the trad method of one at a time...
Yes, though even from mathworld it is spelled as I used: http://mathworld.wolfram.com/Quadruple.html
My question was lame, or showed off how ignorant I am - I am quite rusty - and realized how to do this in mathematica, and in addition sloughed through until I could use the wigner-eckhart...
I'm calculating the zz Component for the quadruple tensor.
Q_{zz} = 3cos^2\theta-1 (r=1 in this case), and the Y_{lm}(\theta,\phi) would be l=2, m=0.
I would like to calculate the result in either maple or mathematica - I have not used either very much - I want to check the result using...
right. I'm not thinking. Of course they can't all be diagonalized. Thanks.
I thought about it as you suggested, clearly y and z are rotated by \cos{\pi}, z-> -z, y-> -y. For the first part of the hamiltonian, obviously S_z^2is unchanged, as is S^2, so its just a matter of the S± terms. I guess...
Monkey,
I guess I'm tired. I looked a bit closer - the problem in the book is quite small. I have a misplaced parenthesis now - so you can do this by inspection, right?
We know the value of S_i is 2\hbar, so that the rotation is then 2\pi, which brings the system back to original.
For S = 2, I have the following hamiltonian,
H=a \left( 2\,{S}^{2}-4\,{S_{{z}}}^{2} \right) +4\,b \left( (\left { S_+}^{3}) +({S_-}^{3})
I'm to show that a rotation of 180º,
e^{-i \pi S_x/ \hbar}
leaves the hamiltonian unchanged.
I started thinking I could use the baker-hausdorff formula...
Hey all,
I have a problem I'm working on. A 2 x 2 ising lattice,
\ H = K_1\sum_{nn}\sigma_i\sigma_j \ + \ K_2\sum_{nnn}\sigma_i\sigma_j \ + \ K_3\sum_{sg}\sigma_i\sigma_j\sigma_k\sigma_l
Were to find H as an explicit function the sigma's...
As you probably know, typical "Caesar breath" calculations show that in each breath we take, there is a large probability that at least one atom is one that Caesar shared.
I have looked at the math here, and find it fairly reasonable - though being able to distinguish between anyone particular...
I think the "new religion" comment to me was meant sarcastically, implying that idea had no merit. Frankly, I don't see any religious connotation; at most, it speaks to the issue that atoms are not "alive", alive in the sense we consider ourselves, :smile: , but that when we bring together a...
I'm about to start a grad level course using Chandler. The brief perusing I've done, I would agree - it appears that it gets directly to the point. As a bonus, tackles modern problems, such as monte carlo simulations.
I had Reif as an undergrad, and still refer to this today - II think...
Also posted in skepticism forum:
Hey everyone,
Currently reading a new book by Bill Bryson, "A short history of nearly everything".
Well, despite the title, clearly even a short history would be a very, very big book, still the read is quite addicting, and there are many scientific...
Hey everyone,
Currently reading a new book by Bill Bryson, "A short history of nearly everything".
Well, despite the title, clearly even a short history would be a very, very big book, still the read is quite addicting, and there are many scientific areas to which I was quite unfamiliar...
Then do it!
I originally received a BS in physics, back in ...um...the eighties
Now I've returned to get my masters, maybe even stay on a bit longer, but in any case, switch fields from animation back to physics, all at the ripe old age of 43. So there...if you really have a dream..you...
Returned to school, masters in physics~biophysics, currently working as computer 3d artist in technical/science fields.
If I could redo, would go back and concentrate on biochemistry, but ah, too old!
Shelley