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Relativistic standing wave electrons?

  1. Feb 28, 2016 #1


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    Gold Member

    Quote from the wikipedia article of relativistic quantum chemistry:
    "... These corrections affect the electrons differently depending on the electron speed relative to the speed of light. Relativistic effects are more prominent in heavy elements because only in these elements do electrons attain relativistic speeds"

    I don't understand this. How can there be relativistic quantum chemistry effects if the electrons that orbit atoms are standing waves?
  2. jcsd
  3. Feb 28, 2016 #2


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    Staff: Mentor

    The expectation value ##\langle \hat{p}^2 \rangle \neq 0##, so while it is a standing wave, the electron has momentum. Actually, the first-order correction to the energy of the electron due to relativistic momentum is ##- \hat{p}^4 / 8 m^3 c^2##.
  4. Feb 28, 2016 #3


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    I have got the impression that due to your depiction of an electron as a standing wave, you assume that it stands still around the nucleus. The thing is, that "standing wave" is the wavefunction of the electron. This wavefunction contains the information about the momentum probability distribution around the nucleus. Despite the average momentum being zero, the electron can actually be spotted moving when its momentum is being measured. So, it can have non-zero momentum actually.
    EDIT: DrClaude beats me to it.
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