In a Hilbert-space whose dimensionality is either finite or countably infinite, we have the discrete resolution of identity
\sum_n |n\rangle \langle n| = 1
In many cases, for example to obtain the wavefunctions of the discrete states, one employs the continuous form of the resolution...
Thanks for your replies, I have not had time yet to look into this more. I still think it's an interesting question, but my original motivation for it has disappeared, since I realized that a contour integral around a delta-function singularity will give 0, by simply looking at the definition of...
Does the Dirac delta have a residue? It seems like it might, but I don't know how to attack it, since I really know very little about distributions. For example, the Dirac delta does not have a Laurent-expansion, so how would you define its residue?
Hi,
For single-electron atomic systems, the electron can be specified by four quantum numbers n, l, m_l, m_s (principal, orbital, z-orbital, z-spin). The orbital quantum numbers are well defined since the problem is spherically symmetric.
However, for many-electron systems, the spherical...
I think one should not take the virtual particles too literally. Terms that look like intermediate particles (propagators) show up in the perturbation expansion of the interaction between two interacting external particles. However, their energies are allowed to take any value, not just those...
The Feynman slash
\slashed{a}=\gamma^\mu a_\mu
maps a four-vector a to its Clifford algebra-representation. This is a linear combination of the gamma matrices with the components of a acting as expansion coefficients. What physical significance does this new object have?
The gamma...
What is meant by saying that the Goldstone-bosons are "eaten" by gauge bosons?
I've seen this statement all over, but can't find a good explanation of what this actually means. Anyone care to shed some light?
K^2:
What do you mean by "at a distance"?
Do I understand you correctly like this:
* Prior to any electron/positron annihilation, a positronium bound system forms.
* This formation releases radiation.
* After formation, annihilation occurs, and the particles are effectively at rest...
Yes, that's true, but there are higher-order diagrams contributing in which one or more photons are exchanged before annihilation. So theory can take into account the Coulomb interaction, but the question is whether the energy shows up in experiments.
Yes, but that doesn't really answer my question.
I mean, if the energy balance of a process is out of order, it seems to me that the physics community would be well aware of it, trying to find a solution. Since this debate obviously doesn't exist, I imagine that the person who told me is...
When an electron and a positron annihilate, they typically produce two gamma rays, each of energy mc^2 plus whatever kinetic energy available before annihilation. I was recently told that it is an experimental fact that the electrostatic energy between the electron and the positron does NOT...
Thank you humanino for that answer. I'll have to think about it for a while.
Of course, you're right about the momentum-position stuff! Got a little mixed up in the old head...