What is meant by overlapping wave functions?

Answer 1

Pretty much the same thing as when ANY type wave activity overlaps.

If a fluid wave from one source meets up with wave in the same fluid, but from a different source, you have overlapping waves. The result can be interference, both destructive and constructive.

The same thing happens when you have EM waves (ie, light) coming from two different sources. This can happen if the EM radiation has a wavelength of one meter (ie, radio waves) or one angstrom (x-rays), or anything in between.

Erwin Schroendinger hypothesized the usefulness (existence?) of a wave function, which can be used to accurately predict the behavior of sub-atomic particles. It has been found that, when predicting such behavior, one can assume that this wave function also acts like a fluid wave or a EM wave. You can accurately predict maxima and minima of the probability of an electron, over time, reaching a specific point in space given two possible paths for that electron. Simply assume that the two possible paths of the electron are like sources of this wave function, then assume the two wave functions overlap (just like other waves), and then do the math -- and, at the end, you have an accurate prediction of the probability that an electron will reach somewhere.

Scientists still debate just what this MEANS -- is this wave function something REAL, or just a mathematical trick that just happens to work? No matter what the case, assuming an overlapping wave function is like other overlapping waves, allows us to predict what will happen.