A wave function is a mathematical tool, a function that when squared and taken the integral of gives the probability of finding a particle in a certain area. The function itself however has absolutely no meaning. This wave function only has values in certain ranges, but can give probabilities for finding a particle outside of the area we would expect to find it, this is quantum tunneling and has been proven.

What I feel is misunderstood here is that although a particle can be everywhere within a certain range, that range has a limit (sometimes the function just approaches zero, and mathematically still gives an extremely small answer far from the area we confine the particle in (for example an atom) but these values are incredibly small, so physically this has no meaning (I really mean so small you can't even comprehend it, and that's still for areas relatively close to the area we confine it in)

So while the particle can exist in an area rather than a point as a wave, this doesn't stretch as far as people seem to think. As a side note, the wave function for a particle is different to its debroglie wave length. The first has no meaning, the second does, but describes something else.

I hope I didn't anger anyone here ^.^ maybe I assumed you guys saw it this way when you meant something else. In any case I hope I taught someone something

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