Recent content by tasos

in pion's system from this results we conclude that is going to decay before it reach the bottom. This 1/7 you say its the problem. But given the average free path in the water ,i think i need to calculate some probability. For example if i had a beam with $$N_0$$ pions, given the average path...

Homework Statement Charged pion with average life time $$\tau=10^{-8} sec$$, and mean free path in the water$$\ell=100m$$ falls prependicular to a lake (depth of lake is at $$\ell_0 =30m$$ with velocity $$V=0.9999c$$ What of the next is correct? 1). The particle isn't gona touch the bottom of...

Ok sorry. So here the energy interval between adjacent J levels is $$ΔE_{FS}= E_J -E_{J-1}= \beta J$$So for J=4 we have $$ ΔE_{FS}= E_4 -E_{3} = 4 \beta $$ so here $$ \beta =42,75 cm^−1$$ and for J=3 we have $$ΔE_{FS}= E_3 -E_{2} = 3 \beta$$ so here $$ \beta =72 cm^−1$$ANd if I am correctly...

Homework Statement [/B] We have that the three lowest energy states of a system are $$ ^3F_2, ^3F_3, ^3F_4 $$ (these are the Term symbols) with relative energy gap $$0,\ 171,\ 387 \ cm^{-1}$$ Now using the perturbation $$H_{LS}=\beta \ \vec{L}\cdot \vec{S}$$ i have to find the best value of...

Also I've seen a lot of exercises with angular momentum that we use\hat{n}l But in general case with no given value of l i can't see how i can work this out.

if we use the Hamitlonian operator on the YLM basis we get \hat{H}|Y_l^m> = \dfrac{b}{a}(1-i)l_+ + \dfrac{b}{2}(1+i)l_- + al_z(l_z + \dfrac{b}{a} )|Y_l^m> = c_-\dfrac{b}{a}(1-i) Y_l^(m+1) +c_+\dfrac{b}{a}(1+i) Y_l^(m-1) + (a\hbar m^2 + b\hbar m)Y_l^m So i sould demand that the Y_l^(m-1)...

new calculations showed that [\mathcal{L}^2,\mathcal{L}_+]\neq0 does not commute, so i don't see how this process can help. Vela i don't understand. Whats the method you are saying i must follow.

Homework Statement We have the hamiltonian H = al^2 +b(l_x +l_y +l_z) where a,b are constants. and we must find the allowed energies and eigenfunctions of the system. Homework EquationsThe Attempt at a Solution [/B] I tried to complete the square on the given hamiltonian and the result is: H =...

Homework Statement (a) Find the energy eigenvalues and eigenfunctions for this well. (b) If the particle at time t = 0 is in state Ψ = constant (0 <x <L)). Normalize this state. Find the state that will be after time t>0 (c) For the previous particle, if we measure the energy at time t = 0...