Recent content by Arnd Obert

This is great, thank you very much! You are completely right with your assumption about the many particle system. Now the last part remains: When evaluating the geometric series, I get a density of states which looks like $$\Omega(\epsilon)=\frac{1}{2\pi}\int dk\exp\left(N\left[ik\epsilon-\ln...

The End of #3 is the correct result but I have to find the way to get there. Thank you! I will try the tensor products.

When multiplying $$e^{ikE1} \cdot e^{-ikH}$$ you get $$e^{ikE} e^{-ikH}$$ because ##e^{ikE1}## is diagonal, isn't it? And then you can pull it out of the trace? Thank you a lot, but now it got even worse: This Hamiltonian should be inserted $$H = \sum_{j=1}^{N}\hbar\omega(a_j^{\dagger}a_j +...

Hello, I'm stuck with this exercise, so I hope anyone can help me. It is to prove, that the density of states of an unknown, quantum mechanical Hamiltonian ##\mathcal{H}##, which is defined by $$\Omega(E)=\mathrm{Tr}\left[\delta(E1\!\!1-\boldsymbol{H})\right]$$ is also representable as...

Hey you all, I'm new here and looking forward to having a good time in this forum. My name is Arnd, studying physics in the 10th semester and working on my master thesis in NMR geophysics right now. Cheers