Thank you for the reply.
Indeed, it is well accepted in the electron microscopy community as well as other society that the electron described here could be treated as a single electron and could be described by the Dirac equation or relativistic Schrodinger equation of free electrons (e.g...
Here I listed three references. The first two use Dirac equation and the last one mass-corrected Schrodinger equation. But they all do not taken the electric and magnetic field self-interaction into Hamiltonian. The experimental set-up are the same as in PRL 109, 254801 (2012).
[1] PRL 99...
A single electron can form a vortex itself. So the vortex needs not come from someplace.
So you are suggesting that two vortex beams are interacting with each other via electric field? But as I recalled the Boersch effect, it was treated completely as electric field interaction between...
I reread the paper and found that the authors claimed that "Note that the fields are due to the charge and current arising from the flow of electrons associated with the vortex and we assume that electron-electron interactions are negligible, thus ignoring the Boersch effect":confused: Any idea?
I agree that for a contiunous emittion of electrons, the electrons will interact with each other. I tried to calculate the space-charge effect in electron microscopy but failed to get a reasonable value.
But I still have the question that the Hamiltonian of single electron, if we have taken the...
:cool: This argument is reasonable but I don't think it's applicable here.
I just made a simple calculation. For a 200 kV electron, its speed is about 0.7c. Assuming that the cross-section of the beam is 1x1 angstrom^2 and the current density about 1 nA taken from the reference, then we can...
Well, it does deal with free electrons. The electric field [Eq.(9)] and magnetic field [Eq.(10)] of the vortex beam are all evaluated from the solution of Schrodinger equation of free electrons [Eq.(1)]. Then ,the authors claim that "To determine how electric and magnetic fields interact
with...
Sorry, I cannot open the wiki page because of some reasons. But it works for me now.
I've sent the reference link to you by private message. Thank you.
Thanks for the reply.
Anyhow, the interaction due to the virtual photon should not enter the Hamiltonian as e\boldsymbol{\sigma}\cdot\mathbf{A},\boldsymbol{\mu}_e\cdot\mathbf{B} and -eV? Sorry I know little of QED.
In that paper, the authors simply added e\boldsymbol{\sigma}\cdot\mathbf{A} and...
Hi, everyone :)
Recently I've read a paper and found in that paper that the authors derived the wavefunction of moving free electrons from its own electric and magnetic field. It was quite a shock to me.
So, for free electrons without external electric and magnetic field, why additional...