# Recent content by Mutatis

1. ### Show the formula which connects the adjoint representations

Well, this is one exercise from my quantum mechanics class...
2. ### Show the formula which connects the adjoint representations

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...
3. ### Net force acting on a charged particle ##+Q##

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?
4. ### Net force acting on a charged particle ##+Q##

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.
5. ### Net force acting on a charged particle ##+Q##

They're still exerting force over ##+Q##, but as they're are diametrically opposed to each other, so they cancel out. Right?
6. ### Net force acting on a charged particle ##+Q##

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...
7. ### Find the eigenvalues and eigenvectors

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}##.
8. ### Find the eigenvalues and eigenvectors

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.
9. ### Find the eigenvalues and eigenvectors

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}##.

13. ### Find the electric field at an arbitrary point

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...