The information about a particle is contained in a vector of unit-norm called the wave function. One postulates says that this wave function is supposed to evolve with time as the particle interacts with other particles (by being in the potential field generated by other particles).
A measurement of a state variable, like position, is equivalent to an interaction of a particle, with a measurement apparatus specifically designed to change the wave function of the particle into one of the position eigenstates.
So there's no special phenomenon like a "wave function collapse". The measurement is just an example of an interaction, i.e. an interaction which evolves the wave function into an eigenstate of the variable being measured. The wave function doesn't collapse, or cease to exist after the measurement. The wave function just evolves in time, as usual.
I often see proposed explanations for the wave function collapse (decoherence is something I remember). What's all that about? The "collapse" seems to be just the usual evolution of the wave function. Can someone explain why the collapse is so mysterious?
Best Answer
The collapse becomes `mysterious' once you realise that:
You have (very, very broadly) two solutions. Either you decide that there are special physical systems called "measuring apparata" that obey different rules of evolution than the rest of quantum systems. Or you say "everything can go in a superposition." Both options are weird, and hence "the problem" and the endless debate on interpretations.
[Edit to include @MikeScott's comment]
There is a third option, namely, to say that "quantum mechanics is incomplete, there must be a better theory describing what is actually going on". This option also leads to weirdness, and so did not put a stop to the endless debate.