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comment What's the role of classically forbidden paths in path integral?
It doesn't have to be the "smallest value of S", classical paths must only be extrema of the action functional
comment Connection between Poisson Brackets and Symplectic Form
Thanks for the clarification. It still doesn't make any sense to me why they chose such confusing way to present this, but at least I understand what happened now. I do have to say though that in my version of the book (also from 1998) the matrix you have in eq. 5.43 is for $ \Omega ^{-1}$ not $\Omega$, and as a result your matrix after "we conclude..." should be $ \Omega $. It doesn't change anything else you pointed out, but could create confusion for someone else.
comment Connection between Poisson Brackets and Symplectic Form
I do not see how you answered the confusion exposed on my post. I know the matrices representing the PB and the symplectic form are inverse to one another, the problem lies on their representation, i.e., in the (q,p) representation w^{ij} have to be the matrix elements of the symplectic matrix so we get the right expression for the PB (if the order of the \xi are q1,q2,p1,p2, for example). Whereas, if I use w_(ij) as the matrix elements of the inverse of omega to obtain the symplectic form I get (again in the q,p rep), w = - dq ^ dp instead of w = dq ^ dp.
comment Number of conditions for a two-particle state to be decomposable
$x$ is supposed to represent a three dimensional vector. Sorry if that was unclear, maybe I should have written it in bold.
comment Phase shifts in scattering theory
"For a typical potential" is a very vague statement. It would be better perhaps to say "in the limit of low energy scattering".
comment Chaos theory and determinism
What a great answer. Reminds me that I need to keep coming back to this website.
comment Why is quicksilver (mercury) liquid at room temperature?
@Georg Any thoughts on the more specific and detailed argument I have in my answer now?
comment Why is quicksilver (mercury) liquid at room temperature?
One more thing: even after disconsidering VB or MO theories, the concept of valence shell remains being important. Wavefunction methods will either be perturbation, or expansion of possible electronic configurations, in which the characteristics of the atoms (such as their valence shell) will determine the probability for distinct electron configurations in the expansion and also the most important corrections in perturbation theory. Of course if you want, you can only do the math or computation and get your results without worrying about any of this, but I believe the point here is clear now.
comment Why is quicksilver (mercury) liquid at room temperature?
@Georg The major explanations in the link are based on calculations, experimental facts and models such as the ones given by quantum mechanical molecular orbital theory and the Dirac equation. Quantum Mechanical MO theory, or even old and modern valence bond theory, though inaccurate in not capturing full electronic correlation, are powerful ways to interpret chemistry, specially when the predictions of those and experiment are alike. The concept of filled valence shell for the properties of Hg is important in all of those (Dirac eqn, MO, and VB theory). I wonder what else would you want.
comment What is the mechanism of dielectric saturation?
Thank you for the insights. So, if I understood it correctly, the lack of orientational freedom, i.e., rigidity of the first solvation shell molecules, in the presence of the field created by the ion, makes solvent molecules less prone to reorganize themselves, and hence orientational polarization response decreases, reducing the experimentally measured dielectric constant for this same region. I'd say this makes perfect sense.
comment Why are the noble metals inert?
@Georg: That's certainly true, and that's what I meant by saying that it is better not to reduce the arguments to simple gas-phase electronic configuration trends. By the way, just to make it clearer, the inaccurate arguments I mentioned are the ones made by Carl Brannen, not by Georg. I completely agree with Georg's statements.