Entropy measures the number of microscopic states of a given system.
For a pure state, the count is one. Thus, entropy ~ log(1) = zero.
However, on the other hand, if we calculate the entropy of finding a particle in real space. It will not be zero. 
My question is, what is the entropy of such pure state? Is it zero or not? Then what about my idea to calculate it in real space distribution?
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