Recent content by Narcol2000

The book is Mathematical Methods for Physics and Engineering by Riley. Pretty decent book overall but this particular section on convolution is a bit naff to be honest, it makes more sense after having understood the more general definition in the link i posted above. As a stand alone intro to...

Thanks for clearing that up, saying that f(x) is an experimental observable yet having a definition that restricts f(x) to being a pdf is a recipe for confusion! I sought out a derivation http://cnx.org/content/m10085/latest/ along the lines of what quadraphonics suggested and i must say i...

I having a hard time understanding an aspect of the definition of the convolution of two functions. Here is the lead up to its definition... It goes on to discuss what the observed distribution h(z) will be if we try to measure f(x) with an apparatus with resolution function g(y). And tries...

yeah i found the mistake, I get the numerator to be 2((-1)^{n-1} - 1) which does lead to the right answer. thx for your help.:cool:

I'm trying to find the Fourier series of |sin x| between -pi and pi. I've got it down to: a_n = \frac{1}{\pi} \int^{\pi}_{-\pi} |sin x| cos (nx) dx which i wrote as: a_n = \frac{2}{\pi}\int^{\pi}_0 sin x cos (nx) dx writing sin x cos (nx) = \frac{1}{2} (sin (n+1)x - sin (n-1)x) I...

Ah i see that explans the difference of a factor of two between the regular coefficients and complex coefficients... thanks

Why is the complex Fourier series expanded from +\infty to -\infty. Yet the regular Fourier series from 0 to +\infty?

Thanks atyy, makes sense. :)

I'm trying to follow the idea behind Lagrange multipliers as given in the following wikipedia link. http://en.wikipedia.org/wiki/Lagrange_multipliers I follow the article right up until the point where it goes: 'To incorporate these conditions into one equation, we introduce an...

If one has a diatomic molecule with energy levels \epsilon_l = \frac{h^2 l(l+1)}{2I} l = 0,1,2,3,4,5... if the degneracy is given by g_l = (2l+1) How does one show that the Helmholtz free energy at low temperature (h^2/Ikt large) is given by F = -3kT e^{-h^2 / IkT} + ...

Ah of course, in my haste i forgot the obvious fact that classical thermodynamics was established before the statistical treatment was even investigated. So the statistical definitions are just chosen so they correctly correspond to the classical thermo definitions. Thanks :)

What is the reasoning behind defining the helmholtz free energy as F = -kT ln Z? I always wanted to know why it was just defined as the above. Is it as a form of convenience because the macroscopic theromodynamic observables of a system at constant temperature (ie the canonical ensemble) are...

Thanks a lot those notes are also pretty useful in other respects as well.

Given the mean energy of a system in a heat bath is \bar{E} = - \frac{\partial ln(Z)}{\partial \beta} Where Z is the partition function and \beta = k_BT Why is the standard deviation of E defined by: (\Delta E)^2 = \frac{\partial^2 ln(Z)}{\partial \beta ^2} I can't seem...

Thanks for the tip, it makes sense now, I just hate learning things without knowing the reason behind it.