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.
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Sign up to join this communityIn 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.
Consider the 1D case for simplicity.
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.