Recent content by Morto

Ahah. Thank you for your help. What about for the Hamiltonian H = \sum_k \left(\epsilon_k - \mu\right) c^{\dag}_k c_k + \gamma \sum_{kp} c_k^{\dag}c_p Can I use the same method to determine the ground state? What does this Hamiltonian represent?

Nope, I was just given that Hamiltonian and told to find the ground state, the energy of the ground state E_0 and the derivate wrt \mu, so if E_0 = \epsilon_k - \mu then \frac{\partial E_0}{\partial \mu} = -1. (and if E_0 = 0, then obviously the derivate is zero). Is this a 'famous' result?

Ah, yes, of course. H_k = \epsilon_k\left(\begin{array}{cc}1&0\\0&0\end{array}\right)-\mu\left(\begin{array}{cc}1&0\\0&0\end{array}\right) = \left(\begin{array}{cc}\epsilon_k - \mu&0\\0&0\end{array}\right) So calculating the eigenvalues det\left(\begin{array}{cc}\epsilon_k -...

Okay, so the matrix representation of these operators is c^{\dag}c = \left(\begin{array}{cc}0 & 1 \\ 0 & 0\end{array}\right)\left(\begin{array}{cc}0 & 0 \\ 1 & 0\end{array}\right) = \left(\begin{array}{cc}1 & 0 \\ 0 & 0\end{array}\right) And the Hamiltonian of the kth term will be H_k =...

Homework Statement I have been given the Hamiltonian H = \sum_{k} (\epsilon_k - \mu) c^{\dag} c_k where c_k and c^{\dag}_k are fermion annihilation and creation operators respectively. I need to calculate the ground state, the energy of the ground state E_0 and the derivative...

I'm seeking some clarification on a topic found in Jackson 'Classical Electrodynamics' Chapter 5. This deals with the magnetic field of a localised current distribution, where the magnetic vector potential is given by \vec{A}(\vec{x}) = \frac{\mu_0}{4\pi}...

Can I consider the line of charge as a sum over an infinite number of point charges?

How? That works with the symmetry of parallell plates, but there is no such symmetry here.

So, I've solved many problems involving parallel sheets of conductors (finite, semi-infinite, and infinite) and also finite sheets at a given angle to each other. I can post the results to these if it may be useful, but I'm more interested in sheets that are perpendicular. Consider a...

I'm not sure whether to post this in the Mathematics or Physics forums, but I figure this problem is easily reduced to its transformation irrespective of the physics it describes. Consider a semi-infinite sheet of (infinitely thin) conductor charged to a potential V. It is placed at a distance...

Hello! I need to calculate \int_{-\infty}^{\infty} x^{2} e^{-\frac{|x|}{b} dx and I know the answer should involve \pi. I've tried splitting the integral for x and -x with limits from 0 to infty and -infinty to 0, which gives me the answer of 2b. But I don't think this is correct. Does...

Hello! Sorry to hash up this very old thread, but I need help with this exact problem and I don't understand the solution given. I'm trying to find the integral of x2exp(-x2 / a2) from -infinity to infinity. I've done what's recommended here, but I end up with a double integral of 1/4...