"If we add the volume probability densities for the three states for which n = 2 and ℓ = 1, the combined probability density turns out to be spherically symmetrical"

Somehow my brain rejects this... Could somebody kindly explain how combining those 3 states gives a spherically symmetric blob ?

Question

"If we add the volume probability densities for the three states for which n = 2 and ℓ = 1, the combined probability density turns out to be spherically symmetrical" 

Somehow my brain rejects this... Could somebody kindly explain how combining those 3 states gives a spherically symmetric blob ?

ganeshie8 · Answer

attachment

ganeshie8 · Answer

spherically symmetric means the probability must be same over the sphere at r everywhere

kainui · Answer

Well if you have the mathematical form for these, you can add 'em up

ganeshie8 · Answer

but those 3 geometric shapes don't seem to give me a full solid sphere ?

ganeshie8 · Answer

for example

m = 0 is along z axis
m = 1 and m = -1 are along y axis

there is nothing along x axis

ganeshie8 · Answer

thats just one of the details,
if i overlap the 3 graphs, it gives some shape like this : 

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