The electron is a stationary wave, called stationary state

Why do electrons in an atom occupy only the stationary states?
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Why does an electron not emit energy when it is in a stationary state?
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They are stationary waves, like the electrons and photons and are seen as "particles" only when they are "seen" .

I kind of think the stationary state thing is just because it's not meaningful or practical in most cases to track the trajectory of an electron while it moves about. So they use knowledge of the potential & kinetic energy to determine where it possibly can move & just assume it has a certain probability of being there because it moves so fast (faster than we can practically measure).

Honestly, QM looks like a statistician got a hold of physics and beat it with an ugly stick.

When you learn classical physics, you start out with Newton's laws of motion, including F = ma. Then you learn how to calculate position, velocity, & acceleration as a function of time. E.g.

v = at
x = ½at² + v0 t + x0

Then you learn about the Euler-Lagrange equation which lets you determine an object's motion just by knowing the potential & kinetic energy of the system. In some cases, it's much simpler to use. Same sort of thing with the time-independent Schrodinger equation, etc.