Recent content by robotopia

There may be much better ways of doing this, but here's what I would do. First, I would treat p as being the parameter over the whole path (i.e. p=0 means that the point is at the beginning of the first line, and p=1 means that the point is at the end of the last line). Then I would work out...

Before showing the theorem, I'll first establish the lemma that if you have two real 2x2 matrices, and if you multiply them on the right by \begin{bmatrix} 1 \\ i \end{bmatrix} and you get the same result for both, then the two original matrices are the same: Let X= \begin{bmatrix} x_1 & x_2...

Let me recast the statement of my question in purely mathematical terms. Let S = \{(a,b)|a,b \in \mathbb{R}; a>0; b>0\}. Define a function F:(S \times S) \rightarrow \mathbb{R}, and define a relation \sim on S such that two elements s_1,s_2 \in S are related s_1 \sim s_2 iff F(s_1,s_2) =...

Transitivity is a purely mathematical concept. I think physicists would be less likely to understand it than mathematicians. If ~ is some relation, then transitivity is the statement that if a~b and b~c, then a~c. "Transitivity of thermal equilibrium" just means that if some physical system A is...

I've just started reading Chandrasekhar's Introduction to the Study of Stellar Structure, and I'm having trouble following one of his mathematical assertions. Rather than quote the relevant parts in their entirety here, I've typeset them and linked them...

I'm looking for feedback on my answer to the following question (if my proof has holes in it, etc.) In particular, I've tacitly assumed that ψ is real. Does this extend naturally to complex ψ? Or don't I have to worry about that? Problem 2.2 from Griffiths' Intro to QM: Show that E must...

Quite right, Mordred. I just stumbled on this paper which, though it is talking about surface density profiles, confirms what cepheid says: Summing masses between r1 and r2 and dividing by annulus area is the same as integrating mass density over the z (axis of rotation) direction, right? Or...

Thanks Mordred. Not a popular question to answer, it seems... :-)

I'm tending to think that #1 is correct, and that it's synonymous with "column density". Can anyone confirm?

Hi everyone, I'm trying to understand circumstellar disks. One term that keeps cropping up in this context is "surface density". The disks, though flattened, are still three-dimensional, so I'm confused about what "surface density" actually means. I can think of a couple of possibilities...

Thanks again, Chronos. The article is helpful, but will require more careful reading to find the answer I'm looking for. I feel as though there's something basic that I'm missing, but I can't quite put my finger on it. I'll post again if I have any luck.

Planck Mission results seem vast... Thanks, Chronos, for the reply. I made my way to http://www.sciops.esa.int/index.php?project=PLANCK&page=Planck_Published_Papers, tried to find something specifically relating to my question, and failed, feeling overwhelmed by the sheer amount of their...

In this 1984 paper on circumstellar dust, the author says, speaking of the emissivity/absorption of dust grains at visual and infrared wavelengths: My question is: where did the expression ##\lambda_p / 2\pi## come from, and what is the physical justification for it? I understand that small...