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...