Preparing a 15 000 words popular science mini-book for publishing

I need a native speaker to check grammar, punctuation and sentence structure and correct all needed. The book is about quantum physics but the text is quite simple and the scientific terms are my responsibility. If some places would still be questionable I want us to discuss them all. I also want the freelancer to be ready to discuss places rewritten by him if I have questions about them. The bigger sample is in attachment and here is another smaller part for example: "The Heisenberg matrix can be imagined as a chessboard with the atomic nucleus in the centre and with a great number of cells around it. Obviously, these cells are not flat or located all on one plane as on a regular chessboard, but spread out in space in all directions around the nucleus; to be more precise, this 3D chessboard has spatial cubes filling the entire 3D volume of the atom. Some cubes are “forbidden”, which corresponds to earlier notions of forbidden space between orbits, and electrons may be imagined jumping from one “allowed” cube to the other in tricky ways. But in the words of the new physics, it is not the electron that is jumping from cube to cube, but its highest probability to be found in a cube. As for Schrödinger, development of a convenient mathematical language is his greatest contribution to quantum physics. However, this language gives the impression that micro reality is more similar to the usual everyday macro reality (to the visions of classical Newtonian physics) than it is in thoughts Bohr and Heisenberg. Schrödinger’s mathematical description of the then-discovered wave state of particles by means of differential equations is analogous to the classical physics’ description of water waves or, rather, sound waves, so many scientists decided that more classical explanations of quantum phenomena had to be developed. However, this trend proved to be a waste of time and effort of many scholars that lead to a deadlocked, while a more exotic direction continues to be successful even today. In fact, it became clear over time that very precise and convenient mathematics of Schrödinger should not be discarded, but it cannot serve as a proof that the microcosm is similar to our macro world."