Can the wave function of an electron be divided and trapped?

Nov 6, 2014

Credit: Mike Cohea/Brown University

By Science Daily

Electrons are elementary particles — indivisible, unbreakable. But new research suggests the electron’s quantum state — the electron wave function — can be separated into many parts. That has some strange implications for the theory of quantum mechanics.

New research by physicists from Brown University puts the profound strangeness of quantum mechanics in a nutshell — or, more accurately, in a helium bubble.

Experiments led by Humphrey Maris, professor of physics at Brown, suggest that the quantum state of an electron — the electron’s wave function — can be shattered into pieces and those pieces can be trapped in tiny bubbles of liquid helium. To be clear, the researchers are not saying that the electron can be broken apart. Electrons are elementary particles, indivisible and unbreakable. But what the researchers are saying is in some ways more bizarre.

In quantum mechanics, particles do not have a distinct position in space. Instead, they exist as a wave function, a probability distribution that includes all the possible locations where a particle might be found. Maris and his colleagues are suggesting that parts of that distribution can be separated and cordoned off from each other.


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3 comments on “Can the wave function of an electron be divided and trapped?

  • The research is viewable here. Unfortunately, the LaTeX of Eq. (5) has malfunctioned; it’s meant to say that h=0 at early times.

    It is my view that Science Daily’s coverage of this story has two key oversights. One is that this finding is not so much something with strange implications for quantum theory as one of the strange implications of standard quantum theory. The other concerns the final question (i.e. if an electron is found in one bubble, what happens to any others which had a partial share in its wavefunction)? I think this question is more straightforward than the article would suggest; the probability distribution for the electron’s location updates (so that its probability of being somewhere other than its observed location is 0, at least initially). That kind of learning-about-distant-places trick has been found in quantum effects before.

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    Lorenzo says:

    Sadly, I can’t access the original article -well, I could if I paid, but I’m currently too broke for that…
    So, let me see if I grasped the problem right (“understand” is a word that hardly applies to QM, thus I won’t use it… especially without reading the full research article).
    It seems to me that they have found a way to cleverly exploit the tunneling effect(*)…

    Presmise: the electron is forbidden to actually enter the liquid Helium due to the fetching of a mirror charge on the surface, with which it (the electron) creates a bound state -if you put an electron in a classical electric field from a poin charge, such as the mirror it creates, it will accomodate itself in bound state-, and the surface tension of the liquid.
    If you force the electron inside the volume, since it cannot roam inside the liquid, it will create a tiny bubble around itself… at least, this seems to be the case (I’m no expert on the effect, so I rely on what I read in the past 5 minutes).

    If you found the way to split this bubble into some fragments, close enough to each other for the wave function to tunnel(*) through them, thus having a non-zero probability of finding the elctron being in a bound state with its mirror in each of them, it is concievable that all of these bubbles where the electron can be due to the tunneling effect, will stay in place until “something” happens that makes the electron more likely to be into one rather than another. Actually, since there is no way of making the electron collapse into one single bubble (if you’re skilled enough in creating them) without further interventionon from the observer, the elctron must be assumed to be in all of them, thus they must be there -and it would be rather disturbing to see them burst.

    And, if you stop for a second, you really can’t help being amazed by the beauty of non-relativistic Quantum Mechanics. And all the Math that makes the theory possible.

    At least, this is what I think is happening based on the scarce information I can gather without paying for the original article.

    (*)Because the particle behavior is described by a wave, and this wave is the solution of an equation (the Shroedinger Equation, in this case) that depends on the potential, if the potential’s “walls” aren’t infinitely high, you can have a “leakage” through the potential wall -although the particle wouldn’t have enough energy to classically go over the wall.

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