I read somewhere that a quantum field can be thought of as a tiny bowl at every point in space with a ball doing SHM (quantum harmonic oscillator). It was given that the amplitude of this SHM is quantized, and each quantum signifies a particle. (i.e. if the ball rolls with minimum amplitude, there are no particles in that point of space. If it has the next amplitude, then there is one particle and so on).
What I don't get is how this analogy relates to quantum fields which are not exactly quantized at every point of space. For example, a single electron has a wavefunction spread out over some space. At every point in this space, we can say that "there is a fraction of the electron over here". But, If I model this as a bunch of oscillators, I can't have a fraction of an electron as the amplitude of SHM, as its supposed to be quantized.
I'm quite sure there's a flaw in my interpretation, but I can't figure it out. Could someone give a more detailed explanation of quantum harmonic oscillators?
Note that I do not understand the mathematics behind quantum mechanics, so though I don't need layman's terms, I would rather stay away from the equations.