Some books about QM include big warning about "Mathematics is not Physics!" at very beginning, but nobody reads it. Chapter 2 The Formulation of Quantum Mecha

Some books about QM include big warning about "Mathematics is not Physics!" at very beginning, but nobody reads it. Chapter 2 The Formulation of Quantum Mechanics 2.1 Basic Theoretical Concepts Every physical theory involves some basic physical concepts, a mathemati- cal formalism, and set of correspondence rules which map the physical concepts onto the mathematical objects that represent them. The correspondence rules are first used to express a physical problem in mathematical terms. Once the mathematical version of the problem is formulated, it may be solved by purely mathematical techniques that need not have any physical interpretation. The formal solution is then translated back into the physical world by means of the correspondence rules. Sometimes this mapping between physical and mathematical objects is so obvious that we need not think about it. In classical mechanics the position of a particle (physical concept) is mapped onto a real number or a set of real numbers (mathematical concept). Although the notion of a real number in pure mathematics is not trivial, this correspondence rule can be grasped intuitively by most people, without any risk of confusion. The mathematical formalism of quantum mechanics is much more abstract and less intuitive than that of classical mechanics. The world does not appear to be made up of Hermi- tian operators and infinite-dimensional state vectors, and we must give careful and explicit attention to the correspondence rules that relate the abstract mathematical formalism to observable reality.