# How to calculate probability of finding an electron at a point?

In school i learned how to calculate probability of finding electrons in some volume but how can we calculate the probability of finding a electron at a particular point.

Point here has negligible volume.

• The probability you want is $0$. – Ivan Neretin Jun 1 '16 at 13:37
• An electron doesn't have any meaningful presentation of being at a point. At that level the world is inherently fuzzy, so it does not make sense to talk about where an electron is. With the quantum mechanics used in chemistry, the best interpretation we can have is: in which region is the electron likely to be present? – Ali Caglayan Jun 1 '16 at 15:56

The modulus square of the wavefunction is interpreted as a probability density in the sense that $$|\psi(x)|^2\mathrm{d}x$$ gives you the probability of finding the electron in within $x$ and $x+\mathrm{d}x$. Now if you want to consider the probability to find the electron exactly in $x$ you have to take the limit $\mathrm{d}x\to 0$ and this gives you zero probability. Formally, this corresponds to compute $$P(x=x_0) = \int_{x_0}^{x_0} |\psi(x)|^2\mathrm{d}x = 0,$$ which is zero since the limits of the integral are the same. Therefore there is $0$ probability to find an electron at exactly one point.