For obtaining the probability distribution we should take the absolute value of the Schrodingër Wave Function 'Ψ'and then square it. But why to take first the absolute value if the square is going to give us a positive number anyways?

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    $\begingroup$ see for details mathworld.wolfram.com/AbsoluteSquare.html $\endgroup$
    – anna v
    Nov 18 '16 at 5:41
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    $\begingroup$ The wave function can be complex, for example $\psi(x)=Ae^{-x^2/2\sigma^2+ikx}$. Squaring that won't even give a real quantity, let alone a positive one. That's where the absolute value kicks in, it turns a complex function into a real one. In this case $|\psi(x)|^2dx=|A|^2e^{-x^2/\sigma^2}dx$, which now has the physical interpretation of a probability distribution density. $\endgroup$ Nov 18 '16 at 7:27

This is because the values of the wavefunction are complex numbers. Squaring a complex number doesn't necessarily give you a positive number, or even a real one. For example, $i^2=-1$, and $(1+i)^2 = 2i$.


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