# Search results

1. ### 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...
2. ### 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...
3. ### Find the eigenvalues and eigenvectors

Homework Statement Find the eigenvalues and eigenvectors of the following matrix: $$A = \begin{bmatrix} 3 & 0 & 0 \\ 0 & 3 & 2 \\ 0 & -1 & 0 \end{bmatrix}$$ Homework Equations Characteristic polynomial: $$\Delta (t) = t^3 - Tr(A) t^2 + (A_{11}+A_{22} +A_{33})t - det(A) .$$ The Attempt at...
4. ### Find the electric field at an arbitrary point

Homework Statement A distribution of charge with spherical symmetry has volumetric density given by: $$\rho(r) = \rho_0 e^{ \frac {-r} {a} }, \left( 0 \leq r < \infty \right);$$ where ##\rho_0## and ##a## is constant. a) Find the total charge b) Find ##\vec E## in an arbitrary point...
5. ### Find the normalization constant ##A##

Homework Statement Find the noralization constant ##A## of the function bellow: $$\psi(x) = A e^\left(i k x -x^2 \right) \left[ 1 + e^\left(-i \alpha \right) \right],$$ ##\alpha## is also a constant. Homework Equations ##\int_{-\infty}^{\infty} e^\left(-\lambda x^2 \right) \, dx = \sqrt...

9. ### Write the matrix representation of the raising operators...

Homework Statement Hi, guys. The question is: For a 3-state system, |0⟩, |1⟩ and |2⟩, write the matrix representation of the raising operators ## \hat A, \hat A^\dagger ##, ## \hat x ## and ##\hat p ##. Homework Equations I know how to use all the above operators projecting them on...
10. ### How can I find the wave equation u(x,t) of a string

Find the wave equation U(x,t) of a vibrating string with linear density d, tension p, initial velocity zero, weight L and initial displacement U0(x) = a1*sin(2*pi*x/L)+a2*sin(4*pi*x/L). Guys, please help me with this task. I did the following procedure: The U(x,t) solution must me a sum of...