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I Superposition of an electron

  1. Oct 16, 2016 #1
    Does a superposed state of an electron exist over a larger amount of space than the state of an electron as a particle?
     
  2. jcsd
  3. Oct 16, 2016 #2
    You would have to define the boundary conditions, energy etc of the system to answer.
     
  4. Oct 16, 2016 #3

    DrClaude

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    I don't understand what you mean. Can you rephrase the question?
     
  5. Oct 16, 2016 #4
    I am comparing the particle version of an electron to the electron in a superposition of possible states. The particle is assumed to be concentrated in one region and not in a superposition, and the particle has experienced decoherence. On the other hand, the electron described by superposition is mathematically composed of a linear combination of states, and I am wondering if those states are thought to exist over a wider range of space than in the space that the particle exists.
     
  6. Oct 16, 2016 #5

    vanhees71

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    The point is that you can't say a vector is "in superposition". A vector is a vector. It can be decomposed into superpositions of any other vectors. A particularly important superposition is to express the vector as a linear combination with respect to a basis, in QT most conveniently in terms of a orthonormal basis. You have to specify which basis you mean to say which "superposition" you mean.
     
  7. Oct 16, 2016 #6

    PeroK

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    I think you are fundamentally misunderstanding the QM nature of an electron. Do you have in mind the state of a free electron after a measurement of its position?
     
  8. Oct 16, 2016 #7
    I have in mind the state of a free electron as it travels through space. Such an electron would be in superposition with itself, right?
     
  9. Oct 16, 2016 #8

    PeroK

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    That statement makes no sense to me. How much QM do you know? Are you learning it yourself?
     
  10. Oct 16, 2016 #9
    I am currently learning QM on my own, yes.

    Maybe that statement would make more sense in the context of the double slit experiment for electrons. If one electron travels through a double slit diffraction grating, one of the conclusions from that experiment is that the electron interferes with itself when the electron is not measured.
     
  11. Oct 16, 2016 #10

    PeroK

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    Are we talking about a free electron or the double-slit experiment?

    One last question: do you have a text book? If not, what are you using to learn QM?
     
  12. Oct 16, 2016 #11
    Double-slit experiment. Sorry for the confusion.

    I have David Griffith's Introduction to Quantum Mechanics.
     
  13. Oct 16, 2016 #12

    PeroK

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    What's your question about the double-slit experiment?

    This makes no sense to me and suggests you haven't understood the concept of a wave function or the supporting mathematics. For example:

    An electron is a particle and is fully described by its wave function, which is a function of time and position and represents the state of the particle.

    How far have you got with Griffiths?
     
  14. Oct 16, 2016 #13
    I have read the first three chapters of Griffiths. I have watched some online lectures from universities as well.

    If I remember correctly, decoherence is equivalent to wave function collapse. This decoherence, which is a consequence of measurement, causes a particle to be observed.

    In the context of the double slit experiment, before measurement at a phosphorescent screen, the particle is mathematically described by a wave function that is a linear combination of states. One conclusion from the double slit experiment is that the electron must behave like a wave in order for the diffraction pattern to appear at a phosphorescent screen. By definition of a wave, this wave has to take up more space than the particle version of an electron that only travels through one slit, right?

    I would also like to know how the wave behavior of the electron is linked to the wave function of the electron -- is the wave function of the electron the same as the wave behavior that must occur in order for a diffraction pattern to appear? If so, I think that would imply the wave function of an electron exists across more space than the wave function for the particle version of an electron.
     
    Last edited: Oct 16, 2016
  15. Oct 16, 2016 #14

    PeroK

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    What you have written, IMO, shows the influence of pop-science videos! None of that could come from Griffiths, not least because:

    a) He doesn't use the term decoherence.

    b) He doesn't cover the double-slit experiement.

    c) He never talks about a particle having "wave-like" behaviour or the wave-particle duality.

    One answer:

    The wave function of a particle is not the same as a particle having "wavelike" behaviour. That is a fundamental misunderstanding on your part.

    And one suggestion:

    I would stick to Griffiths and learn QM from him (that's the real deal) and forget the pop-science videos you've been watching.
     
  16. Oct 16, 2016 #15
    Alright, thank you for pointing that out! I'll need to be more careful with what I accept as facts.
     
  17. Oct 16, 2016 #16
  18. Oct 16, 2016 #17

    PeroK

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    As I said, Griffiths does not explain or use the term "wave-particle" duality. What it doesn't mean is that an electron is "sometimes a wave and sometimes a particle".

    Try this:

     
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