Superposition and Coherence in quantum physics

[neelakash]

I want a clarification in the idea of superposition principle.Perhaps,I should rather say that the distinction of superposition principle in QM and in classical physics.

Few weeks back,I was spending time with Gottfried's book. He explains the novelty of superposition principle with the help of a two state system.He does this as for one particle systems, the superposition principle has some classical analogue,he comments.You can take a look at the experiment described in his text; it is available at google book review (Kurt Gottfried,p14).It took some time for me to digest the experiment,and I have written something in my blog:http://www.gradqm.blogspot.com/

But my present question is how superposition principle for one particle system [QM] (say, double slit experiment with electrons) different from the superposition principle in classical optics.In classical optics,the superposition occurs between two waves (generated from the different parts of the wavefront of the same primary wave) and interference effect is produced by the variation in the cross term(real of course).
In double slit experiment in QM(with photon or electron or whatever),we can reach a situation where a single state is exhibiting interference.It is interpreted as the actual state is a linear combination of two base states:
$$\psi\ =\ a\ |1>\ +\ b\ |2>$$
And interference occurs between the two base states beyond the slit.Here, the probability amplitude $$\ <1|2>$$ is complex.It looks conceptually similar to the classical optics to me.Am I missing something?Or is it that the wavefunction is complex and that is making all the difference?

While going through the same,I also found that the idea of coherence is modified in QM.In particular,Gottfried comments that coherence has a richer meaning in multi-particle system,which he did not explain.I found some rigorous treatment in Ballentine's book (many body theory).But what I want is some simpler way to look at it.How to conceive the meaning of coherence in double slit experiment and how it is different from its meaning in classical optics.And what possible modification is needed when we consider multi-particle system.Can anyone shed some light?

 

[0xDEADBEEF]

The answer that comes to my mind goes along the lines that you cannot decohere a photon easily. If you send a particle through a slit and you manage to hit it with a photon along the way you can upset its phase in a random manner, destroying the coherence pattern. The second answer is "Aharonov Bohm effect"

 

[neelakash]

Can you be a little elaborate?

The superposition looks the same to me in single particle interference whether in classical physics or in QM.My question is for single particle interference,are they the same? It is often said that superposition principle in QM is different than in classical optics.

What did you mean by the "2nd question"?

 

[0xDEADBEEF]

The second answer is also for the first question.

Particles don't interfere classically, waves do. The superposition principle is a fact about systems described by linear equations. If you want to get an intuitive feeling for quantum mechanical interference maybe you should read the third part of the Feynman lectures.