How Was Quantum Entanglement Theoretically Predicted?

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Schrödinger had proved/predicted QE theoretically prior to experimental (though not loop-hole free) verification.

the theory also firmly predicted that QE could not be used to send instantaneous signals.

the theoretical understanding/prediction of QE was there prior to experimental observation (?)

Question- What knowledge/logic was used to prove/predict QE theoretically? - explain in layman's terms/language

i.e. what body of QM knowledge, rudimentary observations were known prior to bell's tests?
 
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Nothing is ever "proved" theoretically - QE was first shown to be a consequence of the schodinger equation as "Bell's Inequality" (iirc)... which you know. Presumably, therefore, you know the history - so your question does not make sense.

Perhaps you imagine that QE theory must have been predicated by some sort of observations? afaik this is not the case - rather it came about as a result of attempts to disprove or find limits to QM. (I think the earliest was in the EPR paradox).
 
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If we release an electron around a positively charged sphere, the initial state of electron is a linear combination of Hydrogen-like states. According to quantum mechanics, evolution of time would not change this initial state because the potential is time independent. However, classically we expect the electron to collide with the sphere. So, it seems that the quantum and classics predict different behaviours!
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