Recent content by Mutatis

Well, this is one exercise from my quantum mechanics class...

That's my attempting: first I've wrote ##e## in terms of the power series, but then I don't how to get further than this $$ \sum_{n=0}^\infty (-1)^n \frac {Â^n} {n!} \hat B \sum_{n=0}^\infty \frac {Â^n} {n!} = \sum_{n=0}^\infty (-1)^n \frac {Â^2n} {\left( n! \right) ^2} $$. I've alread tried to...

I'll try to write up this when I get home. This exercise have got my brain confused. At the first question that I've posted, would you, if you were my physics teacher, consider it right?

In the first case, the net force is going to be a sum of the individual contributions of each charge acting over ##+Q##, superposition principle. And then if I was left with 10 equally spaced charges the system is going to equilibrium state.

They're still exerting force over ##+Q##, but as they're are diametrically opposed to each other, so they cancel out. Right?

Homework Statement Twelve equal particles of charge ##+q## are equally spaced over a circumference (like the hours in a watch) of radius R. At the center of the circumference is a particle with charge ##+Q##. a) Describe the net force acting over ##+Q##. b) If the charge located at...

Yes, the values are ##\left( t-2\right) \left(t^2-5t+2\right)##, with ##\lambda_1 = 2, \lambda_2 = \frac {5} {2} - \frac {\sqrt {17}} {2}## and ##\lambda_3 = \frac {5} {2} + \frac {\sqrt {17}} {2}##.

The eigenvector associated to these eigenvalues are ##\vec v_1 = (0,0,0) , \vec v_2 = (0,0,0)##... That's what I've found out.

Yes, ##\left( t-2\right) \left(t^2-5t+2\right)##, with ## \lambda_2 = \frac {5} {2} - \frac {\sqrt {17}} {2}## and ##\lambda_3 = \frac {5} {2} + \frac {\sqrt {17}} {2}##.

Hey guys, I'm here again... I don't know why I'm still having troubles with this kind of subject. I did my readings and so on, but I'm still struggling to get it right... Look, I got another exercise here, I need to find the eigenvalues and eigenvectors of: $$ \begin{bmatrix} 4 & -2 & 0 \\ -1 &...

I've took out ##\rho_0## of the integral because it's a constant...

Oh thank you, I was doing my calculation wrong. So I've tried to do the integrals over r and I got a different answer this time (it doesn't match with the solutionary): $$ E \int_0^r \, da = \frac {4 \pi \rho_0} {\varepsilon_0} \int_0^r e^{\frac {-r} {a}} \, dr \\ 4 \pi r^2 E = \frac {4 \pi...

First I've used the Gauss law, with the information I got from a): $$ E r^2 4 \pi = \frac {8 \pi a^3 \rho_0} {\varepsilon_0 r^2} \\ \vec E = \frac {4 \pi a^3 \rho_0} {\varepsilon_0 r^2} \vec r .$$ The integral of the left side I did under spherical cordinates and the right side I've used the...

Would you please help me to get the right answer for ##\vec E##?

Oh my God... I've done wrong again. The right answer for the eigenvalues is ##\lambda_1= 2, \lambda_2 = 1## and ##\lambda_3 = 3##! Thank you! I'm going to check my calculations before freaking out. I'm so impulsive...