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I don't know how much of what I got out of this book is due to the ten years (!) I spent in college and grad school struggling with these concepts. I think a book like this should be required reading for all physics majors and graduate students. It is my hope that all interested readers would get as much enjoyment out of this book as I did, but it may be that there is just too much pre-supposed knowledge for this to be the case. All I can say is, this is about as clear as quantum mechanics gets.
After reading this book, if you're interested in further material, the late, great Richard Feynman's book, QED, is still the best introduction for the non-specialist. It contains almost no math and Feynman uses mainly spatial concepts to illustrate and explain quantum electrodynamics in a less mathematical, more intuitive way with his usual wit, enthusiasm, and style. The concepts are explained clearly and concisely in a way that is accessible to the layman and non-physicist. After reading this book, if you're interested in a more mathematical treatment, I would recommend the R.I.G. Hughes book, The Structure and Interpretation of Quantum Theory. It uses a little calculus, but mostly sticks to presenting the mathematics of quantum linear algebra, vector spaces, tensors, and matrix theory as developed by David Hilbert specifically for use in quantum mechanics. It's much more technical than Feynman's book but will give you a much better understanding of quantum mechanics in terms of the mathematical theory.