Recent content by gop

So as an mathematical analogy one could say that dU is an exact differential form while delta Q and delta W are not exact (differential forms).

Hi, I have two questions regarding the laws of thermodynamics 1) For example in http://en.wikipedia.org/wiki/First_law_of_thermodynamics the first law of thermodynamics is defined using two different symbols d (as in infinitestimal change) und the symbol delta (which in the article also...

Homework Statement L is the splitting field generated by x^2+x+1 (over \mathbb{Q}) a) Is \sqrt{-3} an element of L? b) Is sqrt(-3) an element of \mathbb{Q}(a), where a is a complex root of x^3+x+1? Homework Equations The Attempt at a Solution Really no idea.

Well , the derivation of T_fi (on pages 79-82) uses the fact that the Schroedinger equation is first order in time. If a second order equation is substituted, a differential equation for the coefficients (a_f) results that is quite different from the simple differential equation that results...

Hi I'm referring to the book Quarks and Leptons (Halzen, Martin). On pages 79-82 nonrelativistic perturbation theory is investigated (i.e. by using the Schroedinger equation, which is first order in time). On Page 85, however, the transition amplitude (T_fi) is used that has been derived on...

@Bob I'm not really sure I'm following your first point. As the cross section increases shouldn't the number of scattered particle increase (everything else being equal). @Vanadium That sounds plausible I guess. I'm still not sure however why this isn't pointed out in the book. Maybe I...

Hi For example in e-e- -> e-e- scattering (electron-electron scattering) the differential cross section goes to infinity as theta goes to zero. Consequently the cross section is infinite. But how can we measure and interpret the cross section/differential cross section and interpret it as a...

A final question. In what order does one approach these subjects up to know I thought first particle physics and then quantum field theory is the way to go. However, I'm not so sure anymore especially since (from looking at e.g. the TOC of Peskin, Schroeder "An Introduction To Quantum Field...

Hi Thank you both for your answer. Maybe you can help me to clarify an additional point. How does the standard model fits into this? The standard model is covered in most particle physics books. So if it is a pretty complete description of nature (except gravity and neutrino mass of...

Hi In Halzen's "Quarks & Leptons" all discussed particle interactions conserve particle number in some sense (Actually particle number is not conserved but if you count the particles minus the antiparticles before the reaction you get the same "particles minus the antiparticles" number after...

Thanks for your answer. Now I'm slightly confused. Actually the example is taken from "Introduction to Applied Nonlinear Dynamical Systems". where it is stated that For any vectors f,g\in\mathbb{R}^n \chi(f+g) \leq \max\{\chi(f),\chi(g)\} where \chi is the Lyapunov exponent given...

Homework Statement Show that \frac{\Vert X(u+v) \Vert}{\Vert u+v \Vert} \leq \max \{ \frac{\Vert Xu \Vert}{\Vert u \Vert}, \frac{\Vert Xv \Vert}{\Vert v \Vert} \} Homework Equations The Attempt at a Solution Tried to rewrite the max statement as an inequality...

ok I got it if I use conditional probabilities I need to use another model and another way to compute the entropy rate. thx

But if I have something like this p(x,y,z)= (1/3,1/3,1/3) then I have entropy 1.585. But now I could have p(y|x) = 1/2 or p(y|x) = 1 as long as p(y|z)=1-p(y|x) the overall probability p(x,y,z) stays the same. So I have the same entropy. But in the case of p(y|x)=1 I can only use two...

Hi The source coding theorem says that one needs at least N*H bits to encode a message of length N and entropy H. This supposedly is the theoretical limit of data compression. But is it? Or does it only apply to situations where only the frequency (probability) of a given symbol is known...