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Questions;

1)

What does infinity mean here? How for do we to go from the center of the atom that infinity is realized and the Quantum World becomes Classsical?

2)

Or in case of a quantum Hormonic Oscillator when does n go to infinity and discrete energy levels disappear?

In Hydrogen Atom

E(n) ~ 1/n(squared)

E(n-1) ~ 1/(n-1)(squared)

At what point in space the classical world starts and quatum world is finished.

Or we do not know how the two world are connected or there is no quantum world because we cannot see it. All of our experiments are purely classical and never quantum so where is the quantum world?