Recent content by jorgen

Hi again, I write the potential energy as (x-m*g/alpha)^2 and then substract the constant which is just a constant so it is not so important - I guess? - then I write it as a Boltzmann mean(x) = \frac{\int_{-\infty}^{\infty}x*exp(-\beta*(x-m*g/alpha)^2}{...

hi, I am defining the displacement from -infinity to +infinity where the Boltzmann weights should be very small for none probable elongations. The potential energy is E = alpha*x^2/2 + m*g*x I need some hints on how to factorize the energy. Thanks in advance

Hi all, I have to determine the mean elongation of a spring with temperature. The spring constant is alpha and the gravitational acceleration is g. I have the following expression for the force F = -\alpha*x +m*g which I can integrate for an expression of the energy E =...

Hi all, I have determined the entropy previously which gives the following results S = k*(N Log N - n Log n -(N-n)*Log(N-n) I have furthermore deduced the relation between state n and the energy as n = \frac{E+N*\epsilon}{2*\epsilon} I know that the temperature is...

thanks, n_1 can change its value that is why I write it like that. So in order to get to 0.5(n+1)(n+2) I have to say that in the limit n = N? thanks in advance

thanks for the reply - my problem is understanding the first summation (N+1)(n+1) how is small n to be interpreted? Thanks in advance any hints appreciated.

Hi all, I have the following sum \sum n - n_1 + 1 which I split up in two independent sums \sum_{n_1=0}^N n + 1 - \sum_{n_1=0}^N n_1 the last sum can be written as 0.5*n(n+1) but how to rewrite the first sum any hints appreciated. The final answer is 0.5(n+1)(n+2)...

so I rewrite the fraction using this hint \frac{(x^2+1)-2}{x*(x^2+1)} I split the fraction into \frac{1}{x}-\frac{2}{x*(x^2+1)} but I can still not see how to rearrange it Thanks in advance Best J

thanks, so I put into one fraction \frac{x^2-1}{x*(x^2+1)} but I don't know how to start rearranging this... Any new hints Best J

Hi all, I have to differentiate Ln(x+\frac{1}{x}) where I first differentiate Ln and than multiply by the differentiation of the inner function 1/(x+\frac{1}{x})*(1-\frac{1}{x^2} which I simplify to \frac{x}{x^2+1}*(1-\frac{1}{x^2}) \frac{x}{x^2+1}-\frac{1}{x*(x^2+1)}...

Hi all, I have to rewrite a serie into a fraction of hyperbolic sine but I am lost... My problem looks like this \Sigma_{n=0}^{\infty} exp(K*F)*exp(-F*B(n+0.5)) which can be rearranged into exp(K*F)/(sinh(FB/2) my problem is I cannot relate the serie...

Hi all, I am supposed to calculate the energy of chain of spins where the magnetic field H = 0. For the first chain the spins are all aligned in the same direction - up - hence the energy U = -NJ where N is the total number of spins. Next, the half the chain is spin up and the other...