The Quantum World at Low Energies

Most of the energy of ordinary matter is carried by atoms. Guided by some experimental observations, and historical accounts, the entire formalism of low energy QM, with the emergence of probabilities, interference, operators with explicit representations, eigenvalue problems, matrices, complex numbers, inner products, superposition principle, vector spaces, Hamiltonians, and the dynamics involved in quantum mechanics, is developed in a unified manner from scratch with no plane waves and no hand waving arguments. It is repeatedly stated that classically, electrons in atoms will radiate and spiral down on the nucleus and atoms would be unstable, and this realization has led to the development of quantum mechanics. That quantum mechanics actually solves this non-trivial problem is proved right here as applied to atoms of arbitrary number of electrons—the so-called multi-electron atoms. Entanglement is treated in detail, involving physical processes exhibiting entanglement awaiting experiments, as well as teleportation, quantum cryptography. We consider as well of the entanglement of apparatus and a physical system, the collapse of a wave function, Schrödinger’s cat, and most importantly you will learn what quantum mechanics says explicitly about matter in bulk and its unusual large extension in space.