Recent content by Paul159

Hello, I would like to understand a relation of this article by Volkov (eq. 4). Let's define the Green function $$ G^{ij}_{ab} (1,2) = -i \langle T_c \Psi_a (1_i) \Psi_b (2_j) \rangle $$ where ##a,b = (1,2)## are the spin indices and ##i,j = (1,2) ## are the indices for the Keldysh contour ...

Hello, I try to solve a time dependent problem described by a Hamiltonian of the type $$ \mathcal{H}(t) = H_0 + V \delta(t) .$$ I started by trying to solve the Schrödinger equation with ##H_0 = p^2 / 2m##, but I'm getting a bit stuck. I would like to know if you know of any books that deal...

Edit : By continuity of ##T(E)## I would say that the good answer is ##T=1##. Also if I end the step potential (I take a potential barrier), the electron coming from the left has to pass the barrier, as it can't change its group velocity. So for me ##T## is always ##1##, even in the pathological...

I have a question about the Klein paradox in the massless case, for a potential step of height ##V_0## (this is exactly the situation described by Wikipedia). I don't have a problem to understand the "paradox", and I think the Wikipedia's illustration is quite telling. My question is : what...

Ok I get it. You have to take two different spinors for ##x = 0## and ##x = a##. The first condition at ##x = 0## will give you the trivial property ##-i = -i##. The condition at ##x = a## will give you ##e^{2ika} = -1##, such that ##k_n = (n + 1/2) \pi /a##. You can lock this topic thanks.

Hello everyone, I have a problem with bounds states of the 1D Weyl equation. I want to solve the Dirac equation ##−i\hbar \partial _x\Psi+m(x)\sigma _z \Psi=E\Psi## with the mass ##m(x)=0,0<x<a##, ##m(x)=\infty,x<0,x>a##. ##\Psi=(\Psi_1,\Psi_2)^T## is a two component spinor. Outside the well...

Ok I see thanks !

Hello, I found this article. In equation (1) the authors wrote that the current operator is given by : ## - \frac{\delta H}{\delta A} ##. I just would like to know if this relation is a just definition or if it can be derived from more fundamentals considerations ? Thanks !

Yes of course, I understand now. Thanks !

https://arxiv.org/ftp/arxiv/papers/1001/1001.4182.pdf (look at the end of page 4).

Hello, I have a question about the creation of the Bell's entanglement state ##1/\sqrt{2} (|HH> + |VV>)##using type I BBO crystals (https://en.wikipedia.org/wiki/Spontaneous_parametric_down-conversion). Two crystals are put orthogonal to each other and each of them emits a photon pair...

I'm referring to the Rabi Hamiltonian model (Jaynes-Cumming model without the rotating-wave approximation). Yes this is exactly what I don't understand (at least I found this terms counter-intuitive). Yes but for strong coupling with matter we cannot neglect them.

Hello, I'm trying to understand the counter-rotating terms of the Rabi Hamiltonian : ##a^\dagger \sigma_+## and ##a \sigma_-##. I find these terms rather strange, in the sense that naively I would interpret them as describing an electron that gets excited by emitting a photon (and vice...

Thank you very much.

Hello, I have a very basic question : why a top quark for example cannot decay into a charm or up quark ? The fact is that I don't really understand where the concept of up- and down-type quark come from (except that they have the same charge). Why a up-type quark cannot transform into...