Schrödinger
If an electron is a wave, where is it?
That time, that place
A young French physicist had made a strange proposal: if light can behave like particles, might particles such as electrons behave like waves?
Schrödinger reasoned that if so, there must be an equation describing how that wave behaves.
Why this question
He wrote the equation and applied it to the hydrogen atom.
Something remarkable followed. The fixed orbits Bohr had simply assumed came out as solutions of the equation, on their own.
And the reason was visible: the wave must fit with itself. It is like a guitar string, which sounds only certain notes because only vibrations that fit the string's length survive.
What was found
A hard question came right behind it: a wave of what?
Schrödinger thought the electron was genuinely spread through space. Born offered another reading: the square of the wave's value gives the probability of finding the electron there.
Not that the electron is spread out, but that where it will be found is settled only as a probability.
Schrödinger never accepted it. His cat was invented precisely to show how strange that reading is.
An electron sat in a definite place on a definite orbit
Permitted orbits emerging from the equation without being assumed
The probabilistic reading became standard and the argument never closed. Einstein rejected it to the end as well