Changes

[[File:norm.png|right|150x250px|thumb|An example of a wave that could be a position function.  (Actual position functions are normally much more concentrated.)]]

[[File:norm.png|right|150x250px|thumb|An example of a wave that could be a position function.  (Actual position functions are normally much more concentrated.)]]

In quantum mechanics, it is impossible to make definite statements such as "the particle is here". This is a consequence of the Heisenberg Uncertainty Principle which (simply put) states that particles move randomly. Thus, the position of a particle is not described as a point but rather as the particle's "position function," which gives the probability that the particle is at any given spot. It peaks at the location where the particle "exists" in the classical sense, and we might [[integral|integrate]] the function over two angstroms around that point and find that there is a 99% chance of finding the particle in that area; however, there is never a 100% chance; the function always has nonzero "tails" everywhere else in the universe. This means that there is always an infinitesimal chance of the particle suddenly "jumping" a foot or even a light-year away from its original location.

In quantum mechanics, it is meaningless to make absolute statements such as "the particle is here". This is a consequence of the Heisenberg Uncertainty Principle which (simply) states, "particles move". Thus, the value of position of a particle meaningless. Instead it is useful to talk about the probable position of a particle at all point. This is what the wave function tells us. As it peaks the probability of finding the particle in that location increases. In the example presented on the diagram where the particle is free to move in 1 direction, we see that there is a region where the particle is more likely to be found. However we also notice that the wave function does not reach zero as it moves towards infinity in both directions. This means that there is a high likelihood of finding the particle around the center, but there is still a possibility, that if measured, the particle will be a long ways away.  

When the particle is actually observed and found to be in a specific location, this wave function has "collapsed" to yield a specific value. However, immediately after that measurement, the particle takes on a new wave function peaking at that location, so scientists cannot keep it collapsed.

When the particle is actually observed to be in a specific location, its wave function is said to have "collapsed". This means that if it is again observed immediately the probability that it will be found near the original location is almost 1. However if it is not immediately observed the wave function reverts back to its original shape as expected. The collapsed wave function has a much narrower and sharper peak than the original wave function.

Scientists have tried but failed to explain why a wave function collapses and predict to which place it will collapse.

Collapsing of the wave function is by no means magic. In can be intuitively understood as this. You find a particle at a particular spot. If you look again immediately its still in the same spot.

 

Luckily accurately predicting how and where the wave function will collapse is a meaningless endeavor. It is the same as trying to say exactly where the particle is which is, as previously stated, meaningless.

===The uncertainty principle===

===The uncertainty principle===