i think it's time to re-indoctrinate the youthpic.twitter.com/tdi0bFAYOA
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Except this is also misleading. The wave function is isotropic around the nucleus.
No, the hydrogen eigenfunctions ψ(r,θ,φ) have nontrivial angular dependence
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The actual wavefunction is a linear combination of the eigenfunctions where the angular dependence goes away. This is intuitive. The atom normally doesn't have the notion of angle.
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what do you mean "actual"? Hydrogen can certainly be in an energy eigenstate .. the energy quantum number doesn't depend on azimuthal quantum numbers, but the angular momentum observables do
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