Recent content by Msilva

Homework Statement A gas has the following equations of state: P=\frac{U}{V} \,\,\,and \,\,\,T=3B\frac{U^{\frac{2}{3}}}{N^\frac{1}{3}V^\frac{1}{3}} where B is a positive constant. The system obeys the Nernst Postulate (S tends to zero as T tends to zero). The gas, at a initial temperature T_i...

I am wondering how can I find the infinitesimal displacement in any coordinate system. For example, in spherical coordinates we have the folow relations: x = \, \rho sin\theta cos\phi y = \, \rho sin\theta sin\phi z = \, \rho cos\theta And we have that d\vec l = dr\hat r +rd\theta\hat \theta...

I need to find a matrix representation for operator A=x\frac{d}{dx} using Legendre polinomials as base. I would use a_{mn}=\int^{-1}_{-1}P_m(x)\,x\frac{d}{dx}\,P_n(x)\,dx, but I have the problem that Legendre polinomials aren't orthonormal \langle P_{i}|P_{l}\rangle=\delta_{il}\frac{2}{2i+1}. I...

Actualy x^3 is an aleatory function that I wrote here just to ilustrate my question, but you helped me a lot. With these integrals the coefficients are exactly those expected by your arguments. This is a hint that the logic of the integral is right. Thank you for your suport, Prayaga.

Hello friends. I need help to write the function x^3 as a somatory using the Legendre polinomials as base. Something like: f(x)=\sum^{\infty}_{n=0}c_{n}P_{n}(x) Basically is to find the terms c_{n}. But, the problem is that Legendre polinomials does't form a orthonormal base: \langle...