Recent content by lakmus

Ok, thanks a lot! I thought that it is quite weird, that the frequency dependence came only from the periodic motion. So could I try to correct this formula by adding proper intensity I in the rest frame - the correct frequency dependence? (I tried to change some parameteres and if the period...

Hi! I try to construct the emission spectrum from relativistic electron rotating in homogeneous magnetic field - synchrotron. In my lecture notes a found out one really easy derivation using the invariance of \frac{I'}{(\nu')^3}=\frac{I}{\nu^3}, where I is the specific intensity and \nu is...

It kind a look like, that treating the pendulum from a statistical point of view does not have any sense . . . But anyway, thanks a lot. Discussion with you really helped a lot.

Yes, sure your right, wrong terminology. So let's have two izolated systems - pendulum and box with gas. We choose some subset of all posiblle states with constant given energy and watch its development in phase space. We agreed that the pendulum will just rotate and nothink else happen. But...

But microcanonical ensamble define by box of gas of certain enenergy will evolving in phase diagram to uniform distribution function, but the microcanonical ensamble define by pendulum at certain energy will not. This is how i get it know, and my intuition says, that not correct . . .

And what about and izolated box with a gas of given energy, where at first is not equilibrium - half slow molecules and half fast, will evolving into more "homogenized" state, right?

I think the same also. But in this case the distribution would not be an uniform - in the definition of microranonical ensamble, is that the system have constant energy and in that case, in equilibrium all state have the same probability, so the equilibrium distribution function is uniform . ...

Ok, well, what if I choose just some (not all) states with exact value of energy. These would be bounded on movement on this equipotencial (in pendulum case some curve). Will these also spread over whole curve, or not?

Hi, I found out this paper http://www.pha.jhu.edu/~javalab/pendula/pendula.files/users/olegt/pendulum.pdf with this animation http://www.pha.jhu.edu/~javalab/pendula/pendula.files/users/olegt/pendula.html At first there is written there, that the area of possible states in some range...

Hi! I have problem with uderstanding of Liouville equation. Which sais that if we have a Hamiltonian system (energy is conserved), then the the volume of phase space is conserved, or equivalently the probability density is conserved (the total derivative of probability density per time is...

You can't imagine, how did you help me! (sure, shame on me - i did just really stupid mistake) But integral from minus to plus infinity I can calculate, so problem solved! Thank you very much.

Well, I get \lim_{n\rightarrow \infty} \int_{\frac{a}{n}}^{\frac{b}{n}} \frac{\sin{y}}{\pi y}dy Right? Actually I tried this before, but what now? Thanks and sorry, if it is obvious, but I can't see it . . I tried do some limit processes, and if sign(a)=sign(b) and the function is there...

Hi, I try to prove, that function f_n = \frac{\sin{nx}}{\pi x} converges to dirac delta distribution (in the meaning of distributions sure). On our course we postulated lemma, that guarantee us this if f_n satisfy some conditions. So I need to show, that \lim_{n\rightarrow...

Thaks a lot for reply. The link explained it to me!

Hi! I try to figure out the probability (sure as function of parameter time) of transition particle in the hole from the first excitation state to the base state in an infinity potential hole. Because the eigenfuncion of particle there are orthogonal, the probability looks like zero -...