The 1926 Schrödinger equation was originally intended to resolve the subatomic quantum particle in an infinite potential field without a word about superposition. Furthermore, E. Schrödinger himself first opposed quantum superposition in his famous paradox "A cat in a box".
However, the giant N. Bohr came with his quantum superposition in 1928 to the Copenhagen conference and announced that he, including himself, who claims to understand it has understood nothing or that he is only a “simple liar”.
We assume that quantum superposition actually solved both atomic chemistry and physics, but this remained a theoretical mystery until the advent of the double-slit interference experiment of a coherent beam of electrons . It has been experimentally proven beyond doubt that quantum superposition exists and works in the same way as described in N. Bohr's interpretation.
The always seductive question arises:
Why is quantum superposition an effective and essential irreducible tool?
The short answer is Yes. The longer answer is that, since the Schrödinger equation is a linear equation, any linear combination of solutions is a solution. Therefore the space of states is the space of all linear combinations.
In the classical limit only a subset of these states exist. But that's just due to the classical limit.
QM just sais that there is some list of observables, identified with eigenvalues of some operator (Schrod, Dirac or Matrix)
and corresponding eigenstate or eigenvector for each. If the system is not observed , you cannot tell in which state it is, so
then you say there is just a superposition of states. If you make an observation, such as opening the lid in the box of the cat, then you do know if the cat is dead or alive. No contradiction. The superposition has collapsed into just one state.
At any rate QM is not supposed to apply to cats.
However this does not seem to carry into all possible experiments. You do electric exitation in a tube containing
Hydrogen, the light comes out containing the frequency of all allowed transitions, you can infer the structure of all eigenlevels at the same time.(not just one). Its not clear that the formulation is 100% in agreement with empirics.
Electron diffraction just indicates the wave nature of particles, not really a "superposition of states".
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