Coherent state

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In physics, specifically in quantum mechanics, a coherent state is the specific quantum state of the quantum harmonic oscillator, often described as a state that has dynamics most closely resembling the oscillatory behavior of a classical harmonic oscillator. It was the first example of quantum dynamics when Erwin Schrödinger derived it in 1926, while searching for solutions of the Schrödinger equation that satisfy the correspondence principle.^[1] The quantum harmonic oscillator (and hence the coherent states) arise in the quantum theory of a wide range of physical systems.^[2] For instance, a coherent state describes the oscillating motion of a particle confined in a quadratic potential well (for an early reference, see e.g. Schiff's textbook^[3]). The coherent state describes a state in a system for which the ground-state wavepacket is displaced from the origin of the system. This state can be related to classical solutions by a particle oscillating with an amplitude equivalent to the displacement.

These states, expressed as eigenvectors of the lowering operator and forming an overcomplete family, were introduced in the early papers of John R. Klauder, e.g.^[4] 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 and are also known as Glauber states.

The concept of coherent states has been considerably abstracted; 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 sometimes referred to as canonical coherent states (CCS), standard coherent states, Gaussian states, or oscillator states.