Quantum mechanics and quantum field theory (QFT) are related but distinct frameworks for describing subatomic phenomena: quantum mechanics treats particles as fundamental, localized point-like entities with well-defined trajectories, governed by wave functions on finite-dimensional Hilbert spaces via the Schrödinger equation, and is inherently non-relativistic. QFT instead treats fields — mathematical objects assigning quantum-mechanical values continuously across spacetime — as the fundamental entities, with particles reconceived as quantized excitations of an underlying field; its dynamics are governed by Lagrangian/Hamiltonian formalisms and relativistic wave equations (e.g., the Dirac and Klein-Gordon equations), operate on infinite-dimensional Hilbert spaces, and incorporate special relativity, enabling particle creation and annihilation that quantum mechanics cannot natively describe. The two theories belong to the domain of theoretical/particle physics, with quantum mechanics recoverable as the non-relativistic limit of QFT, making QFT the more general and comprehensive framework.
Quantum mechanics and quantum field theory (QFT) are related but distinct frameworks for describing subatomic phenomena: quantum mechanics treats particles as fundamental, localized point-like entiti…