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As far as I know, there is a smooth transition between quantum and classical regimes, so that even classical particle like a massive object has a wavefunction associated with it. However, the double slit experiment can either show quantum character, where the particle supposedly passes through both slits and interferes with itself, or classical character, where the particle passes through one slit with no interference. What would a semi-classical particle do when faced with this situation?

In addition, I have a problem imagining a semi-classical particle in general. What is a good example of one?

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What is a "semiclassical particle"? I don't know what that is supposed to mean. The particle always passes through both slits, unless there is something hitting it that kills the interference, so it is always fully quantum. Are you asking for the semiclassical approximation for the double slit experiment? –  Ron Maimon Jul 7 '12 at 5:59
    
I am under the impression that if you take a sub-atomic particle and keep increasing its mass, it eventually becomes a particle that behaves according to classical laws. So, assuming my thought process is correct, what does a particle behave like during this transition? –  Joebevo Jul 7 '12 at 6:07
    
The double slit fringes become closer and closer together, so that it is practically indistinguishable from the particle just going straight through one of the slits with no diffraction. I think it's the single slit that's giving you problems here. For the double slit, the two slits are supposed to be narrower than the wavelength, so that the particle diffracts in all directions. If you make a big object, you'll be hard pressed to move it slowly enough to make a single slit (that it fits through) diffract it in all directions. –  Ron Maimon Jul 7 '12 at 6:35

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There's really no such thing as a semi-classical particle in the sense you're thinking of it. Everything follows quantum laws, even large, massive objects. However, when you have a large number of particles and/or a large number of interactions with the environment, the different parts of the system are not in a coherent superposition. So you can take a statistical average of sorts, and the quantum laws simplify to classical laws.

Perhaps this is better explained with an example: consider trying to send a car through a double-slit apparatus. In principle, you could do it, if you managed to create a coherent superposition of (all the car's atoms going through the left slit)+(all the car's atoms going through the right slit)+(all the car's atoms crash into the wall together) and maintain that superposition throughout the experiment. But in practice, that's not going to happen. The car is going to interact with its surroundings through radiation, vibrations, etc. and also different parts of the car interact among themselves, and that serves to collapse the superposition of left+right long before the car ever makes it to the slits.

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