I have some basic questions on bonds.
Take two identical particles in their ground state. When separated, the Hamiltonian can be written as the matrix:
1 0
0 1
where 1 is the energy.
When brought close together, there is the possibility of transitions through off-diagonal terms, and the...
Actually, I had a misconception. If you have an incoherent source such as a lightbulb, and a single slit that serves as a collimator, then the beam will be collimated. What happens is that you treat each point in your lightbulb as a single source, and this source causes the entire slit to be...
How can there be a range when the atomic transitions are discrete? Doesn't the hydrogen atom only have the Balmer series, which totals 4 lines? So wouldn't the cavity have to be half of one of the 4 lines?
I don't understand how noncoherent light can spread out. I understand the D2/λ figure...
I too am not an expert.
I think it's okay to have a very weak laser, with the amplitude not so high.
How about if you put a very bright light bulb, or many light bulbs, in the cavity? The amplitudes would be very high, and inside a filtering cavity, it will come out monochromatic.
If...
Why is a laser monochromatic? I read somewhere that the reason is because of a Fabry-Perot cavity, and not necessarily because of stimulated emission, so that if you have an ordinary light bulb in such a cavity, it would produce monochromatic waves.
Can you just send the stimulated light...
According to Wikipedia, the residual entropy of ice is Nk*log[3/2], which is less than two equivalent states which would produce Nk*Log[2]. I don't think swapping the hydrogens in a single molecule of H20 counts as a different arrangement. I think you actually have to destroy a hydrogen bond and...
Okay, since everything is in resonance in graphite, then I guess it has no entropy at 0K.
So any crystal would have zero entropy at 0K. If a crystal has defects, it can't even exist at 0K, because only the ground state is occupied at 0K, and the ground state is without imperfections.
Yeah.
I'm used to setting Boltzmann's constant equal to 1, so I forgot to add it.
But if you add it, you get 4.56 J/mol-K.
I'm not a chemist, so I have no clue if that's right or not.
You might get a better answer in the condensed matter physics section, rather than the classical...
I'm not a chemist, but my guess is that diamond has zero entropy, and graphite has:
S=\frac{N}{2} \ln(3)
where N is the number of graphite atoms.
I'm basing this on the fact that diamond is tetrahedral, so all 4 electrons are bonding, whereas with graphite only 3 are bonding in a...
Now that I think about it,
<m(k)m(p)>=(2\pi)^3\delta(k+p)|m(k)|^2
does make sense in the context of 2nd quantization and quantum field theory.
Here you interpret m(k), the Fourier coefficient of the magnetization density field, as the creation and destruction operators of the magnon. That...
Thanks. I think this critical phenomena stuff is interesting. I did the standard calculation of calculating the critical exponents of the van der waals model, and of the ising model in the mean-field approximation (calculating them for the van der waals was slightly hard, but the ising model was...
Yeah it came from Kerson Huang's Statistical Mechanics.
I can actually derive this:
\langle m(k) m(p) \rangle = \frac{\delta(p+k)}{k^2 + \frac{1}{\xi^2}}
from quantum field theory, as this just leads to the Yukawa potential for exchange of spin-0 mesons...
This comes from a textbook, chapter 16 of a book by Huang.
Huang doesn't mention the model other than that it's of a ferromagnet. He uses the relation to derive an "Ornstein-Zernike form".
Anyways, so you're saying that in general, to calculate a correlation, you have to take the trace with...
Does anyone know why:
<m(k)m(p)>=(2 \pi)^3 \delta(k+p)|m(k)|^2
where m(k) and m(p) are the Fourier transform of the order parameter density and the angled brackets <> stand for an ensemble average?
For example, the magnetization M is given by:
M=<\int d^3r m(r)>