Cool, thanks. It looks like that the same series, so is probably the kind of thing that I'm looking for.
Anyone know any good ones to gain an intuitive understanding of other algebraic structures, e.g., rings, fields?
Thanks.
Hello,
A couple of years ago I studied abstract algebra from Dummit and Foote. However, I was never able to gain the intuition on the subject that I would like from that book. I want to study the subject again, and I want to use a different book this time around - one that covers a lot of...
Sorry for bumping this, but I do want to know whether people who have a bit more experience than me with this topic think that my conceptual understanding in the previous post holds water. Any thoughts?
Thanks.
Thanks kith, that's great.
So to make sure I understand you correctly, a simple interpretation that follows from the definition of coherence in the original post would be something like, "coherence between two basis states is a measure of the degree to which those two basis states must be...
Hello,
In the density matrix formalism I have read in numerous places that coherence is identified with the off-diagonal components of the density matrix. The motivation for this that is usually given is that if a state interacts with the environment in such a way that the basis state...
Hello,
I asked this question on math stack exchange as well, it is answered there (or, as of this post, in the process of being answered at least). For anyone who wants to see it, here is the link...
Hello,
I know that the law of the excluded middle is implied in ZFC set theory, since it is implied by the axiom of choice. Taking away the axiom of choice, does ZF set theory (with axioms as stated in the Wikipedia article http://en.wikipedia.org/wiki/Zermelo%E2%80%93Fraenkel_set_theory)...
Hello,
I'm thinking about the wavelength of a freely propagating photon vs. a freely propagating electron.
For the photon, we have the classical picture of oscillating E and B fields perpendicular to the direction of propagation, and we call the wavelength of the photon, which can be...
Hello,
On p.573 of Jackson 2nd Ed. (section 12.1), he says, "From the first postulate of special relativity the action integral must be a Lorentz scalar because the equations of motion are determined by the extremum condition, \delta A=0."
I agree that if the action is a Lorentz scalar, then...
Hello,
Is there a common word in the standard math vocab list (postulate, axiom, lemma, corollary, proposition, theorem, definition, claim, remark, etc.) for something that will be treated as a postulate for convenience, even though it is known to be provable from previous postulates and...
Thanks for the reply, micromass!
I understand - like functions will be in the same quadrant of the complex plane (or even better, "point" in the same direction in the complex plane) at the same time, or restricting ourselves to real functions, like functions will be positive or negative at the...
Hello,
I recently started going through some lecture notes on linear systems and Fourier optics. (By the way, I just started with these, but so far the lecture notes are excellent. If anyone is looking to learn the subject but doesn't want to spend money on a textbook, the lecture notes, and...