Recent content by Uncle_John

Homework Statement We have N non interacting particles in external field \vec{H}. The hamiltonian is given as H = -h\sum^{N}_{i=1}{\sigma_{i}} with \sigma =\pm 1 and h = - \mu |\vec{H}|. Calculate the number of states with given energy E with help of this relation: \Omega =...

Maybe this could help a bit with the second question. Even though the net displacement is 1mm/sec, that doesn't really mean that you have to wait for one second until the first electron pops out from the wire. Reason for that is simple, the number of electrons in your wire pro 1mm is much...

Hey, how can i get a non trivial solution from matrix equation Ax=0 more precisely, i want to calculate eigenvectors : (M- a_1*I)x = 0, i keep getting x=0.

Is it possible to diagonalize such matrix? and how would one do it?

Ok, so it would look something like : w_{x,y}(x,y) = \begin{cases} 0, \text{if } x \in [0,a] \text{and } y \in [0,a] \\ 1/(3a^₂), \text{otherwise} \end{cases} \sigma_{x}^2 = \overline{x^2}...

=>limx->0 ((1-e^x)/x)*1/x+1/x+1 using limx->0(e^x-1)/x=1 =>limx->0 (-1)*1/x+1/x+1 Here you are wrong

w_{x|y}(x,y) = \begin{cases} 0, \text{if} x \in [0,a) \text{and} y \in [0,a] \\ 1/a, \text{if } x \in [0,a) \text{and} y \in [a,2a] \\ 1/(2a), \text{if } x\in [a,2a]...

Yes, sorry, i meant joint probability distribution. So if i follow the formal definition: w_{x,y}(x,y) = w_{y|x}(x,y)w_{x}(x) Then: w_{x|y}(x,y) = \begin{cases} 1/a, \text{if } x \in [0,a) \\ 1/(2a), \text{if } x\in [a,2a]...

Think again about your proposition that x_{3} = x_{1} + x_{2}. If you imagine for a moment that mass 1 is very big, it stands still, so only mass 2 moves. So if mass 2 moves for some distance l, how much does then mass 3 go up or down?

Homework Statement Let's have a box in shape of a square(viewed from the top) from the corner of which a smaller square was cut out.The side of a bigger square is 2a, side of the smaller square is a long. We've got evenly distributed corn seeds all over the box,randomly selected seed is...

you can divide it into components, and then solve the differential equation for each component, that's harder way than just writing the net force balance for the time when speed reaches it's final speed, but you'll learn more from it;)

You could solve this by solving the differential equation that way you'll get the x(t) function, and from there you can calculate the constant or, you could think about the force balance after some time when particle reaches it's final speed

Looking at the t\overline{t} production from: \gamma \rightarrow t\overline{t} so minimum E_{\gamma} = 2m_{t}c^2 But still I don't see how can i get data to calculate \Gamma and M in formula for cross section

Homework Statement Calculate the ratio of scattering cross sections for hadron and muon production \sigma(e^{+} e^{-} \rightarrow hadrons) / \sigma(e^{+} e^{-} \rightarrow \mu^{+}\mu{-}), just underneath and just a bit above the threshold for quark production t \bar{t} (Note only the...

In my books it's written that any integral over a closed loop \gamma equals zero: \oint f(z)dz = 0 But at the same time it says \oint \frac{dz}{z-a} = i 2 \Pi I where I is an index number saying how many times loop \gamma goes around point a. Aren't they contradicting each other? PS: what...