Sorry for the lack of posts recently. Between preparing new quantum mechanics simulations, school getting busier, and the fear of losing my income because of some bickering about budgets, I haven't found the time to post. I return with a "short" post about classical-quantum correspondence. What does this mean? Well, in the real world, we observe things and we can say where things are and what they are doing. However, when we talk about the quantum world, suddenly there this uncertainty! What's the deal?
Why don't small systems behave like what we are used to seeing? Well, as I'm going to show you, they do! Here's a very concrete example of a quantum system that ALMOST looks classical. We return once more to the particle attached to a spring.
As you will see in the videos below, the first is the wave function doing it's wiggly thing. I'm showing this purely to show that the quantum world is a bit more complicated that the classical world, and that a real and imaginary part of the wave function contributes to the probability. The other video shows the main point of this.
Wave Function
Probability Density along with classical path.
You'll notice it isn't melting as it always has been before. I'm not cheating, this is an actual possibility in quantum mechanics. It's called a coherent state, and I picked it because it's a state that very closely follows classical behaviour, but there's still uncertainty in the particles' position.
The vertical line is the probability for a classical particle in the same system. It may not be obvious, but if all of its probability is on a single vertical line (known to physicists as a delta function), then it is at that location with 100% probability! The quantum version isn't just a straight vertical line because of uncertainty! The larger the physical system that that particle is in, the more likely the wave function will look like a vertical line. This is roughly what the concept of quantum decoherance is. The writer of Nano Nook knows a great deal about this, so hopefully we will chime in to correct me or clarify if I said something wrong. Enjoy the movies!
Well, I don't know if I'll ever understand quantum mechanics, but I definitely appreciate the illustrations, and your accessible way of speaking in the posts. I think your audience is probably those who have a more-than-basic understanding of physics, and not the lay public (as we've discussed lots before). In other words, I can sort of get it :).
ReplyDeleteI'm not giving up on you! Hopefully future posts will illuminate what I think the issue is.
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