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What does Wave Function actually measure?

  1. Jun 29, 2015 #1
    From what I understand in laymans terms (Since I am a beginner).

    In quantum mechanics, particles don’t have classical properties like “position” or “momentum”; rather, there is a wave function that assigns a (complex) number, called the “amplitude,” to each possible measurement outcome. The Born Rule is then very simple: it says that the probability of obtaining any possible measurement outcome is equal to the square of the corresponding amplitude. (The wave function is just the set of all the amplitudes.)

    Born Rule: latex.php?latex=%5Cmathrm%7BProbability%7D%28x%29+%3D+%7C%5Cmathrm%7Bamplitude%7D%28x%29%7C%5E2.png

    Couldnt find any diagrams. Could anyone better explain this to me with diagrams?
  2. jcsd
  3. Jun 29, 2015 #2


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    Staff: Mentor

    I'm not sure how it could be made any simpler. You want to find the probability that a measurement will find a particle at a given location, you calculate the value of the wave function at that location, square its magnitude (or equivalently, multiply it by its complex conjugate), and that's the probability you're looking for.

    If this doesn't make sense to you, you'll have to study complex numbers more before you take on QM. Any introductory text on complex numbers will have a diagram that gives an intuitive picture of what is meant by the "magnitude" and "complex conjugate" of a number.
  4. Jun 30, 2015 #3


    Staff: Mentor

    Its like probabilities, in fact along with observables it predicts the probabilities of observational outcomes. In that sense it doesn't measure anything.

    It can be explained and in a quite deep way what's going on - but unfortunately it involves advanced math.

    But just for reference here it is (see post 137):

    The following may also help:

    Last edited: Jun 30, 2015
  5. Jul 1, 2015 #4
    The wave function itself is a mathematical construct - you cannot "observe" a wave function (they're complex in the sense of complex numbers). What you can observe are the eigenvalues of wavefunctions for a given operator, which are used to represent all dynamical variables such as position, angular momentum, etc. Operators act on the wave functions to give you the values you can get when you do perform the measurement. The wave function itself doesn't really "measure" anything.
  6. Jul 2, 2015 #5


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    Staff Emeritus
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    Education Advisor

    The topic is also highly misleading and possibly reflects the OP's lack of understanding. The wavefunction doesn't "measure" anything! Rather, it is supposed to contain the complete description of the system in question, very much like the equation of motion of a dynamical system in classical mechanics.

    The common problem that I have seen with this is that people are trying to run before they learn how to crawl. This is one of the examples where learning classical mechanics first, and getting a feel for what a Lagrangian/Hamiltonian mechanics is in terms of the classical description of a system, may actually be quite beneficial in getting an insight into deciphering the mathematics of QM. Otherwise, one is dangling in mid-air with no lifeline to anything.

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