Recent content by goulio

I tried evaluating the eigenvectors of the matrix filled with ones for M=6 in mathematica and here's what I get : {1, 1, 1, 1, 1, 1}, {-1, 0, 0, 0, 0, 1}, {-1, 0, 0, 0, 1, 0}, {-1, 0, 0, 1,0, 0}, {-1, 0, 1, 0, 0, 0}, {-1, 1, 0, 0, 0, 0}} The first one corresponds t0 \lambda = M...

I found out that the matrix can be rewritten as \left ( \begin{array}{cc}x_1 & x_2 \\ x_2 & x_1 \end{array} \right ) \otimes \left ( \begin{array}{cccc}1 & 1 & \cdots & 1 \\ 1 & 1 & \cdots & 1 \\ \vdots & \vdots & \ddots & \vdots \\ 1 & 1 & \cdots & 1 \end{array} \right ) So I now...

I need to find the eigenvalues and eigenvectors of a matrix of the form \left ( \begin{array}{cc} X_1 & X_2 \\ X_2 & X_1 \end{array} \right ) where the X_i's are themselves M \times M matrices of the form X_i = x_i \left ( \begin{array}{cccc} 1 & 1 & \cdots & 1 \\ 1 & 1 & \cdots &...

I'm considering the beta decay of a neutron into a proton an electron and an antineutrino. I heard that this was observed in 1957 in Cobalt 60. I don't really understand when the antineutrino comes into action... The experimental results say that they detected more electrons in the direction...

Hello, This problem is related to the beta decay of a neutron in a proton an electron and a anti-neutrino. I need to prove that, in the limit where the mass of the neutron and the proton goes to infinity, m_P, m_N \to \infty, we have \bar{u}\gamma^\mu(1-\alpha \gamma_5)(\gamma^\alpha k_\alpha...

Hello, I'm preparing for my condensed matter exam and I'm trying to solve problem 3a) of chapter 22 in Ashcroft & Mermin. The problem is basically to prove that the dispersion relation of a diatomic linear chain will reduce to the monoatomic one when the coupling constants are equal...

You need to find two unknowns, so you need two equations. The key word is "elastic", this means that both energy and momentum are conserved. From this statement you can easily find two equations. But one thing is not clear, you need to know how the sleds collide, do they collide head on, or...

Ok forget about that last one, it is getting late here... It's just the function evaluated at r.

Thank you thank you thank you. Can you tell me how I should differentiate this integral? Thanks again.

Here is another way I tried to solve the equation: Ok here is what I have done for the poisson equation. The gas alone has a Maxwell-Boltzmann Distribution, so the gas under the influence of a conservative potential has the following distribution n(r,v)=n_0(v)\exp(-\phi(r)/k t) where...

What do you mean by this? I'm not sure to get it.

Ok yeah the equation of the gas is a typo and I got wrong the mass enclosed by spherical shell. You're right it is an integral. Actually it is something like: M(r)=\int_0^r du 4\pi u^2 \rho(u) But I put this in the hydrostatic equation I end up with and integro differential equation...

I have the following equation to solve \frac{df}{dx} = -a\frac{f(x)}{x^2}\left (\int_R^r u f(u) du - b \right ) with the boundary condition f(\infty)=0. Any help greatly appreciated.

Hi, I need to find the density \rho(r) of an ideal gas at constant temperature T surrouding a planet of mass M and radius R. The gas is attrated by the planet and is also self-attracting. First, I used the hydrostatic equilibirum equation...