Homework Statement
The problem is to show that
\int_1^x \frac{| \sin(t) |}{t} dt \underset{x \rightarrow \infty}{\sim}
\frac{2}{\pi} \log(x).
The integral is (in case it is important) a Lebesgue integral.
Homework Equations
A theorem is stated which says (I do not currently have the...
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...
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...