I know that because Schrödinger equations solution for probability of that region is 0, but I was looking for an intuitive explanation.

How can you intuitively explain the existence of nodes in an orbital?

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    $\begingroup$ I have no way of knowing what would fit in your mind and what would not. $\endgroup$ Commented Aug 24, 2016 at 16:21
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    $\begingroup$ I don't think kids in high school have the tools to do that @Ivan. $\endgroup$ Commented Aug 24, 2016 at 16:25
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    $\begingroup$ @ahmad The point of all this discussion is, there is another property of matter, which is not intuitive at all. The "property" $F=ma$ is intuitive because we see it everywhere. Schrodinger's equation is another such "property", which is not at all intuitive. It is this property that gives birth to those nodes. You will have to study a little bit of quantum mechanics to understand more of it. Food for thought: "Properties" like the electrostatic force and so on also apply at that scale, along with this new one. $\endgroup$ Commented Aug 24, 2016 at 17:41
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    $\begingroup$ en.wikipedia.org/wiki/Vibrations_of_a_circular_membrane $\endgroup$
    – permeakra
    Commented Aug 24, 2016 at 19:07
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    $\begingroup$ @getafix Let's keep it friendly, please (re: your first comment). Thanks! $\endgroup$
    – jonsca
    Commented Aug 25, 2016 at 0:33

1 Answer 1


It is simply because the wave nature of the functions.

Imagine a tight rope with fixed ends (like a string in a guitar). If you shake it it will vibrate. Both ends remains fixed. If you take a high frame rate video and see it in slow motion, at a fixed horizontal length (let say $x$ positions) the rope will oscillate up and down with some amplitude. It can be seen one or more intermediate $x$ positions that remains always with null amplitude (if it is in state close to a stationary one). There you have nodes in one dimensional string.

Visual example

You would have more complex patterns going to a two dimensional system, and even more in a three dimensional case. They all have nodes, like the 1D case. The 3D case can be represented mathematically by using the spherical harmonics. The angular part of the solutions for the hydrogen atom are those spherical harmonics. The only intuitive explaining that I found is their wave nature. Of course it is not as visual as in the 1D case which is easily found in the daily life. And clearly, what is more weird is the wave nature of matter.

I hope that this answer address your question.

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    $\begingroup$ Just to add to this, the 3D analogue of the "fixed ends" of the rope is the requirement that the wavefunction be square-integrable (aka normalisable), i.e. $\psi \to 0$ as $r \to \infty$. That would explain the presence of the radial nodes, angular nodes are a bit harder to justify imo. $\endgroup$ Commented Aug 25, 2016 at 4:41

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