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Wave function -- Why is there an imaginary part?

  1. Dec 1, 2015 #1
    If wave is a real concept, then why we have a complex(imaginary) part associated with the wave function?
  2. jcsd
  3. Dec 1, 2015 #2


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    It is the squared modulus of the wave function (= a probability distribution) that is of physical interest, since it predicts the likelihood that physical observables assume certain values. The wave function itself cannot be measured and, as far as I know, does not have a physical meaning.
  4. Dec 1, 2015 #3
    Ordinary waves are modeled as complex numbers too though. It's not a quantum-only thing. https://en.wikipedia.org/wiki/Phasor
  5. Dec 1, 2015 #4


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    An imaginary number is not imaginary. That's just a word someone dreamt up one day! Complex numbers are just as "real" as vectors, matrices and continuous functions.
  6. Dec 1, 2015 #5


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    Technically its got to do with the requirement for continuous transformations between quantum states. If a system is in a state and one second later is in another state then we reasonably expect that after half a second it went through some state in getting there. It turns out if you require that then so called imaginary numbers are required:

    BTW they are no more or less imaginary than say negative numbers. You cant point to a negative number of ducks for example. But if you owe someone two ducks then saying you have -2 ducks is very convenient. Same with imaginary numbers. You cant point to square root -1 (doubly so since you cant even point to -1 of anything) but in modelling some things its very convenient to introduce it - QM being a good example.

    Last edited: Dec 2, 2015
  7. Dec 3, 2015 #6
    Classical mechanics can also be described in terms of complex wave functions, so they aren't inherently quantum mechanical things.
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