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I am a mathematics and chemistry double major and I just finished my statistics requirement and a great deal of the class was spent on probability distributions (e.g. Binomial, Poisson, Geometric, Gamma, etc.) and so I was wondering since electrons have a "probability" of being in a certain location according to the Heisenberg Uncertainty Principle, what sort of probability distribution would this represent?

As in, could we treat electrons and their positions as discrete or continuous random variables? And if so, what sort of distribution could we use for an electron being in a particular cloud?

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    $\begingroup$ As a math and chemistry double major, you must have heard of Schrodinger equation and its solutions. These are the distributions you are asking about. $\endgroup$ – Ivan Neretin May 14 '18 at 5:10
  • $\begingroup$ Yeah that's what I figured, I was hoping there would be some strange connection to between stats and chem. $\endgroup$ – djohnson May 14 '18 at 6:30
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    $\begingroup$ There is nothing strange about it (other than the deep inherent weirdness of quantum mechanics, that is). You solve the equation, you get the probability distribution. It is as simple as it gets. $\endgroup$ – Ivan Neretin May 14 '18 at 7:06
  • $\begingroup$ I suppose what I would like to know is what the probability distribution the Schrodinger Equation most closely resembles and whether or not another method to predict electron locations is possible using your average statistical models other than the Schrodinger Equation. $\endgroup$ – djohnson May 14 '18 at 7:17
  • $\begingroup$ Well, the distribution is known and even expressed in elementary function; look and see what it resembles. As for another method, I've never heard of such. Let's wait for someone else's opinion. $\endgroup$ – Ivan Neretin May 14 '18 at 7:38

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