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I don't understand the superposition principle in quantum mechanics or the collapse of wave-function (I think it's impossible for me to understand it) My question is:

Is it possible to demonstrate the quantum mechanical behaviour (Superposition and wavefunction collapse, etc.) in some macroscopic systems under certain conditions so it may be better to understand it? Is it possible to make the wavefunctions of atoms in some material more or less coherent?

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"I think I can safely say that nobody understands quantum mechanics." "Do not keep saying to yourself, if you can possibly avoid it, "But how can it be like that?" because you will get "down the drain," into a blind alley from which nobody has yet escaped. Nobody knows how it can be like that." Both by Richard Feynman. – Keep these mind Jan 18 '13 at 20:13
@Gugg while I get what Feynman was talking about, and understand the virtues of "shut up and calculate," I've never liked the philosophy of giving up all hope of understanding QM in this sense because a group of, admittedly great, minds couldn't work it out back in the 20s and 30s. It's also a stretch to say "Nobody knows how it can be like that." There has been a lot of work on quantum logic etc. recently that seems promising (though I'm far from an expert on the topic). – Michael Brown Jan 19 '13 at 11:21
@MichaelBrown I'll take that as a comment. However, if you want to discuss this (which is quite possible, since I tentatively disagree), I'm game. – Keep these mind Jan 19 '13 at 19:28
@Gugg I disagree with Feynman on this moreso because I'm an optimist and not because I claim any special insight. :) I have no horses in this race. Though I'm personally a fan of Bohmian mechanics (as a handy counter-example to many common claims about the incomprehensibility of QM), I don't particularly "wish it to be true." Nature does whatever she does, and it may very well be that human intuition simply can't grasp it. But I do think it is okay, even healthy, for every generation to wrestle with it on its own terms. We may even find an answer one day. – Michael Brown Jan 20 '13 at 23:59
@Gugg I will agree that there are many traps for the unwary, and many opportunities for laymen thinking about these issues to stumble into "woo" territory - Chopra style b.s. So Feynman's advice is good to a degree. I just don't think it should be an absolute stricture on the style of research people should pursue. All of that said, I spend by far the majority of my time using QM, not thinking about its conceptual foundations. So I'm probably not the best person to be having these debates. :) I think I've said my peace, but if you wish to continue (which I'm happy with), maybe we go to chat? – Michael Brown Jan 21 '13 at 0:07

You've asked two questions. Firstly is it possible to see superposition in macroscopic systems? The answer is yes. This article describes making a tiny "tuning fork" that can be put into a superposition of different vibrational states.

Secondly you ask "Is it possible to make the wavefunctions of atoms in some material more or less coherent?". Again the answer is yes, and a good example is a Bose-Einstein condensate.

As Gugg points out, there is a good Wikipedia article on Macroscopic Quantum phenomena.

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Maybe you'd want to include the Wiki-link from my answer (or not), because I'll remove it (my answer). – Keep these mind Jan 19 '13 at 15:17
Done! Though I wouldn't delete your answer as I think all (except outrageously misleading) answers help illustrate a question. – John Rennie Jan 19 '13 at 16:20

There is a Wiki page on this. I take it that you will never "see" typical quantum behaviour, but quantum mechanics is the only way to explain what you do see (especially in typical QM experiments).

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The basic concept of the collapsing of the wavefunction can be understood be the following Double slit experiment. However my answer does not cover your aspect for a macroscopic question. First focus on basic concepts and than expand your knowledge to the not-so-easy to grasp macroscopic effects. Then consider the beautiful effects described by the John Rennie answer.

Consider reading Double slit experiment which results in a visible pattern. Incident photons/particles have to be considered as a plane wave $\Psi(z,t)$ in z direction. Propability distribution $|\Psi(x,y)|$ of the wave-funkction is proportional to intensity on observation screen.

This experiment performed by Young astonishly can be performed with electrons and even larger particles like neutrons. The conclusion is particles that have to be modelled as waves (under certain conditions). The solid picture of particles still helps in other models.

Interference with oneself

This is easly more confusing. For a start neglect this fact. For advanced understanding of this concept, try to depict the equal experimental result, if one particle at-a-time is used in this experiment. (Somebody can edit an example of this in my answer)

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