"The solution of the difficulty is that the two mental pictures which experiment lead us to form - the one of the particles, the other of the waves - are both incomplete and have only the validity of analogies which are accurate only in limiting cases"

This quote by Werner Heisenberg is referring to the difficulty of understanding the behavior of particles and waves in quantum mechanics. Heisenberg is recommending that the two psychological pictures we form of particles and waves are both incomplete and only precise in specific cases. He is indicating that these two mental photos are just analogies and not a total representation of the behavior of particles and waves. Heisenberg is suggesting that the behavior of particles and waves is more complicated than what we can comprehend with our existing psychological designs. He is suggesting that we need to look beyond our present understanding and develop brand-new designs to better understand the behavior of particles and waves. Heisenberg's quote is a reminder that our existing understanding of the behavior of particles and waves is limited and that we need to continue to check out and establish new models to much better understand the behavior of particles and waves.