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
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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
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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...