Recent content by DevoBoy

Clever! :) So now I end up with the relation: ln|2cos\frac{\theta}{2}|=\frac{1}{2}(ln2+ln(1+cos\theta)) Thanks! EDIT: I'm still not able to use this series to show that \sum_{n=1}^\infty \frac{(-1)^{n+1}}{n}=ln2 Any sugestions?

Ok, so I expand it like this: ln|cos\frac{\Theta}{2}|=ln|1+(cos\frac{\Theta}{2}-1)|=\sum_{n=1}^\infty \frac{(-1)^{n+1}}{n}(cos\frac{\Theta}{2}-1)^n Ultimatly, I want to use this expansion to prove that \sum_{n=1}^\infty \frac{(-1)^{n+1}}{n}=ln2 I can't quite see how this will help...

I'm looking for a series for ln|cos\frac{\Theta}{2}| Using r=1 for my complex variable, if that matters... Any ideas?

You're absolutely right. My mistake. After reading up on Bessel functions (thanks ObsessiveMathsFreak!), I've rewritten my recursion formula as a_{2n}=\frac{(-1)^{n}a_{0}\Gamma(1+3/2)}{2^{2n}n!\Gamma(n+5/2)} which seems to expand beautifully.

I'm trying to solve the differential equation: x^2y''+2xy'+(x^2-2)y=0 using the Fröbenius method. So I want a solution on the form y=\sum_{n=0}^\infty a_{n}x^{n+s} After finding derivatives of y, inserting into my ODE, and after some rearranging: \sum_{n=0}^\infty...

Ofcourse, my mistake. So I end up with solutions: psi_I(x) = A*exp(-ikx) + B*exp(ikx) psi_II(x) = C*exp(-iqx) + D*exp(iqx) psi_III(x) = 0 with boundary conditions psi_I(0) = psi_II(0) (d/dx)psi_I(0) = (d/dx)psi_II(0) psi_II(a) = 0 (loss of continuinity here, right?) Which...

Analytical solutions of S.E. for "unusual" potential Hi, Given the potential V(x)=0, when x<0 (region I) V(x)=V_0, when 0<=x<=a, V_0=real constant (region II) V(x)=infinite when x>a (region III) What would be the general form on the solutions for each region? I...

Hi, I'm baffled by a problem in a quantum physics course I'm taking. Problem: "Use the momentum operator to find an expression for the sum of two planewaves moving in opposite directions. Both planewaves have the same kinetic energy." It's in one dimension only. I know the momentum...