I have a question concerning the stationary states of a spherically symmetric potential (V=V(r), no angular dependence)(adsbygoogle = window.adsbygoogle || []).push({});

By seperation of variables the eigenfunctions of the angular part of the Shrödinger equation are the spherical harmonics.

However, (apart from Y^0_0) these are not spherically symmetrical.

for example: Y^0_1=(3/(4Pi))^{1/2}cos(theta)

So the probability of finding the particle in the xy-plane (so theta=1/2 Pi) is zero (regardless of r).

But why would the probability of finding the particle at in the xy-plane differ from any plane through the origin? (which is due only because of a particular choice of the coordanation axes) How can nature prefer a specific angular direction when the potential is depends only one the distance from the origin?

Isn`t this in violation with the isotropy of space??

BTW: I know LateX, but how do you use it in this posting on this forum?

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# Spherically Symmetric Potentials

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