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Quantum mechanics is a fundamental theory that describes the behavior of nature at and below the scale of atoms. [2]: 1.1 It is the foundation of all quantum physics, which includes quantum chemistry, quantum field theory, quantum technology, and quantum information science. Quantum mechanics can describe many systems that classical physics cannot.
Classical mechanics is a model of the physics of forces acting upon bodies; includes sub-fields to describe the behaviors of solids, gases, and fluids. It is often referred to as "Newtonian mechanics" after Isaac Newton and his laws of motion. It also includes the classical approach as given by Hamiltonian and Lagrange methods. It deals with ...
Geometric optics is an approximation to the quantum theory of light, and does not have a superior "classical" form. When both quantum mechanics and classical mechanics cannot apply, such as at the quantum level with many degrees of freedom, quantum field theory (QFT) is of use. QFT deals with small distances, and large speeds with many degrees ...
The idea of quantum field theory began in the late 1920s with British physicist Paul Dirac, when he attempted to quantize the energy of the electromagnetic field; just as in quantum mechanics the energy of an electron in the hydrogen atom was quantized. Quantization is a procedure for constructing a quantum theory starting from a classical theory.
It is less clear, however, how the classical limit applies to chaotic systems, a field known as quantum chaos. Quantum mechanics and classical mechanics are usually treated with entirely different formalisms: quantum theory using Hilbert space, and classical mechanics using a representation in phase space. One can bring the two into a common ...
Action is significant because it is an input to the principle of stationary action, an approach to classical mechanics that is simpler for multiple objects. [1] Action and the variational principle are used in Feynman's formulation of quantum mechanics [2] and in general relativity. [3]
The end of the first era of quantum mechanics was triggered by de Broglie's publication of his hypothesis of matter waves, [1]: 268 leading to Schrödinger's discovery of wave mechanics for matter. Accurate predictions of the absorption spectrum of hydrogen ensured wide acceptance of the new quantum theory. [1]: 275
The names of action principles have evolved over time and differ in details of the endpoints of the paths and the nature of the variation. Quantum action principles generalize and justify the older classical principles. Action principles are the basis for Feynman's version of quantum mechanics, general relativity and quantum field theory.