Collapse of the wave function, help understand

[Lengalicious]

Ok so when observed, the wavefunction collapses, can someone delicately explain the maths behind it? Or send me to a page with a coherent explanation, that is followable for a first year undergrad? I've covered Eigenvectors briefly in my algebra course last semester and i find that the explanations focus on some eigenvector stuff but i don't completely understand what an eigenvector is, just how to get an eigen vector/value. All i know is that the wave function decreases with path difference and therefore decreases the probability of the particle being at that particular point. But the fact that randomly when a detector interacts with the particle the wavefunction collapses and it acts as a classical particle is confusing me. Whyy? =(

 

[Demystifier]

Ok so when observed, the wavefunction collapses, can someone delicately explain the maths behind it? Or send me to a page with a coherent explanation, that is followable for a first year undergrad? I've covered Eigenvectors briefly in my algebra course last semester and i find that the explanations focus on some eigenvector stuff but i don't completely understand what an eigenvector is, just how to get an eigen vector/value. All i know is that the wave function decreases with path difference and therefore decreases the probability of the particle being at that particular point. But the fact that randomly when a detector interacts with the particle the wavefunction collapses and it acts as a classical particle is confusing me. Whyy? =(

The wave function does not really collapse. It only splits into distinguishable branches, so that any branch does not know about the existence of the others. The right question is why can't we see all the branches at once?

One possible answer is - because we ARE one of the branches (many-world interpretation).

Another possible answer - because we are made of little particles which end up in one of the branches (Bohmian interpretation).

There are also other possible answers, but nobody knows which one is correct.

If you want more math behind it, see e.g. Sec. 2 of
http://xxx.lanl.gov/abs/1112.2034