 in physics, in quantum mechanics, a coherent state is the specific quantum state of the quantum harmonic oscillator whose dynamics most closely resembles the oscillating behaviour of a classical harmonic oscillator. it was the first example of quantum dynamics when erwin schrÃ¶dinger derived it in 1926, while searching for solutions of the schrÃ¶dinger equation that satisfy the correspondence principle.e. schrÃ¶dinger, der stetige Ãbergang von der mikro- zur makromechanik, naturwissenschaften 14 (1926) 664-666. the quantum harmonic oscillator and hence, the coherent states, arise in the quantum theory of a wide range of physical systems.j.r. klauder and b. skagerstam, coherent states, world scientific, singapore, 1985. for instance, a coherent state describes the oscillating motion of the particle in a quadratic potential well (for an early reference, see e.g. schiff's textbookl.i. schiff, quantum mechanics, mcgraw hill, new york, 1955.). these states, defined as eigenvectors of the lowering operator and forming an overcomplete family, were introduced in the early papers of john r. klauder, e.g. .j. r. klauder, the action option and a feynman quantization of spinor fields in terms of ordinary c-numbers, ann. physics 11 (1960) 123â168. in the quantum theory of light (quantum electrodynamics) and other bosonic quantum field theories, coherent states were introduced by the work of roy j. glauber in 1963. here, the coherent state of a field describes an oscillating field, the closest quantum state to a classical sinusoidal wave such as a continuous laser wave. however, the concept of coherent states has been considerably generalized, to the extent that it has become a major topic in mathematical physics and in applied mathematics, with applications ranging from quantization to signal processing and image processing (see coherent states in mathematical physics). for this reason, the coherent states associated to the quantum harmonic oscillator are often called canonical coherent states (ccs) or standard coherent states or gaussian states in the literature. == coherent states in quantum optics == [[image:coherent noise compare3.png|thumb|figure 1: the electric field, measured by optical homodyne detection, as a function of phase for three coherent states emitted by a nd:yag laser. the amount of quantum noise in the electric field is completely independent of the phase. as the field strength, i.e. the oscillation amplitude Î± of the coherent state is increased, the quantum noise or uncertainty is constant at 1/2, and so becomes less and less significant. in the limit of large field the state becomes a good approximation of a noiseless stable classical wave. the 
Quantum_mechanics