Recent content by cosmic_tears

Homework Statement (I copy-pasted the question) Consider N non interacting electrons inside a 3D box similar to the one we saw in class, but this time it is not cubical, i.e. Lx = Ly \neq Lz. 1. Calculate the fermi energy as a function of N;Lx;Lz;me... 2. What happens if we take Lz --> 0...

Thanks, PatF, I realized all ideals are of the form (p^k) for a whole k.

Thanks man. Have some Grog :) \int\sqrt{(4)^{2}} *practicing.

You're welcomed :) By the way - off topic, but - could you tell me how I write formulas here? Do I need some kind of a program, or is it a code, or what? New here...

:) First of all, you don't substruct infinity from infinity :). Secondly, the final expression should be: lim (R-->inf) {R*e^R -e^R - 0 + 1} = lim (R-->inf) {(e^R)(R-1) + 1} Notice that we both got the same answer, only I took out e^R. This way it can be easily seen that this limit gives you...

no, your answer is not correct. you obviously know how to find the derivative using the known formula (and not definition), and you can easily calculate y' to see that y'=6x-6. So that should be the answer you get. Try again, it's an easy limit.

you should know how to calculate this integral. Exchanging variables, you can define u=9t+4. then du = 9dt. = > dt = du/9 So: int {sqrt(9t+4)}dt = int {sqrt(u)/9}du = (1/9)*(u^(3/2))/(3/2). Then stick u = 9t+4 back and use the upper and lower limits. So, to answer your question - it's not...

What do you mean "when calculating I keep getting 1"? You should get: Lim (R-->inf) {(e^R)*(R-1)+1} = inf. How can you ever get 1?

Hello, and thank you VERY MUCH for reading! Homework Statement Let p be a prime number. Let R= Z(p) be the ring defined as followed: Z(p) = {x/y : gcd(y,p)=1} (notice that it's not the ring {0,1,...,p-1}!) I need to characterize all the ideals in this ring, and all of it's quotient...

Thank you for the responses. I'd read them more thoroughly when I have a little more time :)

Well, generally, and usually, physics isn't as rigorous and demanding, at least not on high school level and low degrees levels, as mathematics. However, You can't really study mechanics and understand it profoundly if you don't have the tools of calculus. You can always solve easy problems...

Have you studied calculus? t, delta t and dt for example are all related to time (in your example), but they are totally different, obviously. t is usually a point in the time dimension. t=5, for example, means the point on the "t=5" axis. delta t usually implies a difference between two...

Hello everybody :) Well, I'm past my first Quantum course examination, with a satisfactory grade. Trouble is, there are some really basic things I still don't get, and somehow, everybody seems to shrug when I ask them about it. My profesor tries to explain but I fail to understand, so I thought...

*sigh*... I'm really going to hate them if you're right... :) I'll send a mail to my tutor, all the student are too confused with this subject I guess none have noticed yet. Thank you very much! I'll post here if it turns out otherwise...

But I need an expression consisting only of [A,B], [A,C] and [B,C] I already know that [A,BC] = B[A,C] + [A,B]C...