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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:

[tex]\psi\ =\ a\ |1>\ +\ b\ |2>[/tex]

And interference occurs between the two base states beyond the slit.Here, the probability amplitude [tex]\ <1|2>[/tex] 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?