Elements of Quantum Mechanics

Non-relativistic quantum mechanics is necessarily an approximation to relativistic quantum mechanics. It is valid in the regime where kinetic energies and potential energies (more generally field energies) are much less than the rest mass energies of particles. Following philosophy of Laughlin (2005), I prefer to think of non-relativistic quantum mechanics as an emergent theory: one that is exactly true in the limit of low kinetic and potential energies. Non-relativistic quantum mechanics is such a well verified theory—all modern electronics testifies to it—that it is hard to believe there is not a limit in which it is exact. If there were not such a limit—let’s call this limit the non-relativistic-quantum-mechanics limit (NRQM limit)—then I think non-relativistic quantum mechanics would somehow be a crude theory or model that is sometimes unreliable—which it is not.