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I'm in a superposition of knowledgeable and ignorant until you ask me something, in which case I produce either a good or a stupid answer, depending on various random factors such as whether I'm versed in the general topic, happen to know the specific subject of the question or just get lucky with guessing.
(This analogy breaks apart if you consider the possibility of giving a mediocre answer that's neither accurate nor entirely stupid, which probably makes it the perfect self-defeating counterexample)
Well, technically a solution of a quantum mechanic equation is a projection on a vector space, so a mediocre answer is merely a projection on this <accurate ; stupid> vector space.
So your comparison is actually brilliant!