Recent content by FredMadison

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    Continuous resolution of identity in a discrete Hilbert-space

    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...
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    Residue of Dirac delta function?

    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...
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    Residue of Dirac delta function?

    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?
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    Atomic many-electron configurations and the use of the orbital quantum number

    Ok, got it, this is what I suspected. Thanks a lot!
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    Atomic many-electron configurations and the use of the orbital quantum number

    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...
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    Virtual Photons over Large Distances

    Bill_K: Good point. I try to keep myself from thinking about of what "really" exists. This allows me to sleep fairly well.
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    Virtual Photons over Large Distances

    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...
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    Physical meaning of the Feynman slash

    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...
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    What is meant by saying that the Goldstone-bosons are eaten by gauge bosons?

    Ok, I think I see how this works. Very clear answers, thank you!
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    What is meant by saying that the Goldstone-bosons are eaten by gauge bosons?

    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?
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    Electrostatic energy in annihilation process

    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...
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    Electrostatic energy in annihilation process

    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.
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    Electrostatic energy in annihilation process

    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...
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    Electrostatic energy in annihilation process

    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...
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    Are point-particles real ?

    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...
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