i think it's time to re-indoctrinate the youthpic.twitter.com/tdi0bFAYOA
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Replying to @InertialObservr
Except this is also misleading. The wave function is isotropic around the nucleus.
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Replying to @wood_croft
No, the hydrogen eigenfunctions ψ(r,θ,φ) have nontrivial angular dependence
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Replying to @InertialObservr
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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Replying to @wood_croft
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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Replying to @InertialObservr @wood_croft
I think this may have been the source of confusion all along? A wavefunction in the |n,l,m> basis should not have *azimuthal* dependence (polar is OK), yet yours has both. So it has to be a superposition (I think it’s |7,6,4> + |7,6,-4>).
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There’s nothing wrong with an eigenstate having azimuthal and polar dependence
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Replying to @InertialObservr @wood_croft
Agree, but there exists a “standard” basis set that commutes with Lz, and your function isn’t an element of that set, which might have been what
@wood_croft was trying to say?0 replies 0 retweets 0 likesThanks. Twitter will use this to make your timeline better. UndoUndo
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