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B "Distribution" of a particle in different situations

  1. Apr 7, 2017 #1
    I was thinking about the "distribution" of a particle in space in different situations. An electron bound in a atom have a wave function that is broad.

    What about the broadness of the wave function of conduction electrons in a wire? Or doesn't it even make sense to quantum-mechanicaly speak of conduction electrons in a wire?

    What about the broadness of the wave function of a free electron? By free I mean an electron that is not interacting with any nearby particles or "classical" fields. (I know that just saying nearby is vague (How nearby?), but I hope you understand what I mean.)

    So I was trying to answer myself the two questions above, and I started by thinking this way:

    The time evolution of a wave function is governed by the hamiltonian of the system and I guess the hamiltonian is non-zero only if the system has energy. So in both cases above, I would expect the wave function to be changing in time.
    Also, the broader the wave function, the narrower the momentum function -which measures the distribution of momentum through space-. In the case of the electrons in a wire, I guess they are constantly being atracted by the other charges that form the atoms and by the other electrons as well, but I don't have an idea of how fast they move (in average, at least). For a free electron, it would be easy to conclude that how fast the electron is moving will dictate how broader is its wave function.

    I used the term wave function to mean position function, actually.
     
  2. jcsd
  3. Apr 7, 2017 #2

    mfb

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    The bands are the limits of "infinite" spread.

    Every system has an energy.
    The overall speed of the electron does not matter. You can always change to a frame where its (expectation value of) momentum is zero.
     
  4. Apr 7, 2017 #3
    So that means that the very existence of a particle is dependent on the frame? Because we can change to a frame where its wave function has a different value at a same position in space.
     
  5. Apr 7, 2017 #4

    mfb

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    No. At least not in this context.
    The wave function will look different for different observers, of course. That is not a result of quantum mechanics, you already have different properties in classical mechanics.
     
  6. Apr 7, 2017 #5
    Ok. So, returning to the point of the thread, what can we conclude about the wave function for electrons in a current and for a free electron?
     
  7. Apr 7, 2017 #6

    Nugatory

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    You can conclude that any differences between the two are frame-dependent.
     
  8. Apr 7, 2017 #7
    but certainly there are other important differences
     
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