How do I find the most probable value of position of a (non-Gaussian) wave function? Is it the same value as the expectation value of the position? And is it true that the most probable value of position is equal to the mean for a Gaussian?


The most probable position would be such as where the global maximum of the distribution is located. This is different to the expectation value of a distribution, but it happens that for a Gaussian function the mean and the most probable value are the same.

  • $\begingroup$ So if I have to find the most probable position, then I need to find the derivative of the function and equate it to $0$? How about for most probable momentum? $\endgroup$ – Artemisia Nov 22 '13 at 16:10
  • 2
    $\begingroup$ Yes, derivate and look for a zero. For momentum the same, just you would have to change into that representation first. $\endgroup$ – Ignacio Vergara Kausel Nov 22 '13 at 16:34

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