Why nodes?

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Why nodes?

Post by Chemistry guy on Sat Oct 01, 2016 12:59 pm

We know that there are nodes present in a confined system(like particle in a 1D box).Also psi_n is zero at the nodes and also the probability,psi*psi becomes zero at the nodes. But why are there nodes even present? There doesn't seem any physical reason why a particle cannot be found at certain regions and nodes to even exist?

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Re: Why nodes?

Post by Sabiya on Tue Oct 04, 2016 4:23 pm

If you are searching for a physical reason for nodes to exist, first we need to make physical sense of our wave function Ψ. After we achieve that, we can understand why it needs to have the values that it has at all points, including nodes.
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Re: Why nodes?

Post by Chemistry guy on Tue Oct 04, 2016 7:11 pm

Sabiya wrote:If you are searching for a physical reason for nodes to exist, first we need to make physical sense of our wave function Ψ. After we achieve that, we can understand why it needs to have the values that it has at all points, including nodes.



Since ψ carries "No Physical Significance", your reply suggests that nodes do not carry any physical significance. This does not seem very convincing to me as nodes do carry a physical significance that the particle is NOT found at a node and other relevant things. I am seeking an answer as to why this happens, why are such points(or regions) are ever found?
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Re: Why nodes?

Post by Sabiya on Wed Oct 05, 2016 8:38 am

You interpreted my answer wrong, my friend. Or maybe I wasn't clear enough in my reply.
Either way, I am not suggesting that nodes carry no physical significance, but only that this significance cannot be completely understood without understanding Ψ first.
Of course we can still make some sense of the nodes right now. Like you said, at the nodes we have a zero probability of finding the particle, and it's also a point where the wavefunction crosses the axis (although right now we don't know what difference it makes if Ψ is on one side of the axis or the other).
For a particle in a box, these nodes are created because when two Ψs traveling in opposite direction interfere with each other, they cancel out exactly at a few points, where the net Ψ becomes =0.
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Re: Why nodes?

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