Particles are predictable- one can find the area that they will be in and one can find their speed. If they were chaotic, it would be impossible to find out anything about them, as they would simply be random.

But Chaos plays a big big part. Check Quantum chaos.

I'll give you a point from which you can start from, and that is the Uncertainty Principle. This prevents us from talking about initial conditions in quantum mechanics since we cannot know the position and velocity of a particle simulataneously. The same principle also prevents us talking about trajectories in quantum mechanics because a trajectory is nothing more than a complete description of the position and velocity of a particle at all times.

We can observe a particles position at a certain time, and we can predict the future position from the past data. However, the past of any observed state of a physical system can be mapped in innumerable different ways, giving rise to innumerable different futures.

Could this thread be made into a sticky?