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[[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 meaningless to make absolute statements such as "the particle is here". This is a consequence of the Heisenberg Uncertainty Principle which (simply put) states, "particles move," in an apparently random manner. Thus, giving a definite position to a particle is meaningless. Instead, scientists use the particle's "position function," or "wave function," which gives the probability of a particle being at any point.  As the function increases, the probability of finding the particle in that location increases. In the diagram, where the particle is free to move in 1 direction, we see that there is a region (close to the y-axis) 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.  This is true even if there is a wall at y=5:  it is less likely that the particle will be on the other side of the wall, but there is still a nonzero probability that the particle will "tunnel" through the wall.

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 put) states, "particles move," in an apparently random manner. Thus, giving a definite position to a particle is meaningless. Instead, scientists use the particle's "position function," or "wave function," which gives the probability of a particle being at any point.  As the function increases, the probability of finding the particle in that location increases. In the diagram, where the particle is free to move in 1 direction, we see that there is a region (close to the y-axis) 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 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.

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.