Recent content by Jezuz

What is the relation between a vacuum state in light-front quantization and a vacuum in the equal time formulation? For example, I quantize a free field at equal light-front time and make a mode expansion. The resulting creation and annihilation operators can then be used to define the...

Hi! Has anyone studied the book Quantum Kinetic Theory by M. Bonitz? I am reading it on my own and have a hard time understanding some of the things that are done in the book. Specifically, in the second chapter, he keeps terms which are traces over a commutator. Isn't the trace over a...

You must be very careful when working with operators. Remember that you should always assume that it is multiplied with a function. This means that \mathbf p \times \mathbf A \neq -i\hbar (\nabla \times \mathbf A). Rather we have \mathbf p \times \mathbf A \psi = - i\hbar \nabla...

In the Ising model the spins are allowed to be only -1 or 1 and in a given direction. In the Heisenberg model the spins are allowed to point in any direction.

Ok. I think I have found my error. When I go from the sums to integrals I actually no longer account for the exclusion principle and the result I get in the end is the classical Maxwell-Boltzmann distribution. Apparently the trace in the denominator cannot be calculated exactly. Instead one...

Have you remembered to use the Nabla operator in spherical coordinates when you set up your equations?

Ok. It's been a while since I was working on this, but now I am giving it another go. I will try to be more specific about what I am asking exactly. The problem is: Consider a system of N particles in thermal equilibrium at temperature T . The density operator is then given by: \hat...

I tried that but when the momentum basis is used the partition function is Z = \sum_p \exp(-p^2/2mkT) . I don't know how to evaluate this sum to get the right result. Of course I can assume that the particle is in a large volume V and convert the sum to an integral with a volume factor V/(2\pi...

Hi. Does anyone know if it is possible to start from the thermal density matrix \hat \rho_T = \frac{e^{-\hat H_0/kT}}{\mathrm{Tr}e^{-\hat H_0/kT}} and from that derive that the single particle density matrix can be written as \rho(p ; p') = \delta_{p,p'} f(\epsilon_p) just by...

Let S be a coordinate system fixed on the observer on earth, oriented such that the positive x-axis is in the direction of the motion of ship A. Then in that frame ship A has velocity 0.753c and ship B has velocity -0.851c . Now, we set up a fram S' in which ship A is stationary and...

To find the witdth of the wave packet you should consider the form of |\psi|^2 . This will have the form \psi \propto \exp \left\{- \frac{(z - vt)^2}{A(t)} \right\} This has the form of a Gaussian curve. The maximum occurs where z = vt where the exponens takes on the value 1. The width...

Hmm, the reason to introduce the density matrix is allways to allow for a statistical distribution of states. In some cases however you may use the single or two-particle density matrix when doing calculations on a many-particle system. The density matrix for a particle in a fixed state \psi...

Yepp, a Fourier transform should be used. I don't know if there is any differences between the variables x and r , perhaps not. There is a way to rewrite the levi-civita symbol in terms of delta's, but I can't remember it. This might simplify your calculations somewhat. I will post the...

I read a previous post from you. Your english is a little confusing so it is a little hard to understand what you mean. I think what you should do to calculate C is to require the distribution function to be normalized. So that \int_{-\infty}^\infty f(x,y,z,v_x,v_y,v_z) dx dy dz dv_x dv_y...

What you need to show is that the distribution x \mathcal{P} \frac{1}{x} is the unity distribution. That is, you can multiply this distribution with another distribution without changing it. Alternatively you can show that the effect of using this distribution on a test function \psi is...