How Schro discovered his equation

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I keep reading that Schro's equation was the best one that fit the data. Well, what data was he looking at? I keep waiting to see the data that he analyzed to come up with his equation and I never run into it.
 
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I'm a little skeptical that no one know the answer to this
 
I think the main thing that first convinced people the Schrodinger equation was right was that it predicted the correct spectrum for the hydrogen atom.
 

Thread 'Is a table levitating possible, even at a minuscule probability?'

I am not sure if this falls under classical physics or quantum physics or somewhere else (so feel free to put it in the right section), but is there any micro state of the universe one can think of which if evolved under the current laws of nature, inevitably results in outcomes such as a table levitating? That example is just a random one I decided to choose but I'm really asking about any event that would seem like a "miracle" to the ordinary person (i.e. any event that doesn't seem to...
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