Wave function -- Why is there an imaginary part?

[preitiey]

If wave is a real concept, then why we have a complex(imaginary) part associated with the wave function?

 

[S.G. Janssens]

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.

 

[ddd123]

Ordinary waves are modeled as complex numbers too though. It's not a quantum-only thing. https://en.wikipedia.org/wiki/Phasor

 

[PeroK]

If wave is a real concept, then why we have a complex(imaginary) part associated with the wave function?

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.

 

[bhobba]

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:
http://www.scottaaronson.com/democritus/lec9.html

BTW they are no more or less imaginary than say negative numbers. You can't 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 can't point to square root -1 (doubly so since you can't even point to -1 of anything) but in modelling some things its very convenient to introduce it - QM being a good example.

Thanks
Bill

 

[andresB]

Classical mechanics can also be described in terms of complex wave functions, so they aren't inherently quantum mechanical things.