What does a matter wave truly represent?
Also what is the connection between
Think of matter as very densely packed energy.
The wave function PSI allows one, mathematically, to predict to within a limited certainty, the future status of a system. (We do not have a way to directly observe atomic systems). It contains information about the system.
PSI has no direct physical meaning, it is a precursor to a more useful function called PSI^2. PSI can be positive and negative in sign. PSI^2 however is the probability of finding a particle in space about the atom, and is only positive in value and "lives" in value between 0 and 1.
It is the odds of finding an electron in an atom at a given moment or finding it every at a location in general. This means it gives real physical meaning on position.