Quantum Mechanics (Book)

Quantum Mechanics is mathematically simple compared to the previous two foundations of physics - classical mechanics and fields. It is linear, so no complicated manifolds like in mechanics or relativity. This is deceptive, but is a helpful crutch when first learning the subject. The true nature of quantum mechanics is geometric: the projective geometry of Hilbert space, geometric quantization from classical/symplectic geometry to quantum phase spaces, the moment map in symplectic geometry gives the map to the convex space of probability distributions, and it is also a task to precisely interpret generalized functions, spectra of self-adjoint operators on function spaces, (projective) unitary group representations, and kernels/matrices of these general operators.