# Coherent States

Coherent States

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 Schrödinger derived it in 1926 while searching for solutions of the Schrödinger equation that satisfy the correspondence principle. The quantum harmonic oscillator and hence, the coherent states, arises in the quantum theory of a wide range of physical systems 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 textbook ). 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. . 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 that reason, the coherent states associated to the quantum harmonic oscillator are usually called canonical coherent states (CCS) or standard coherent states or Gaussian states in the literature.

### Other articles related to "coherent states, coherent state, states, state":

Uncertainty Principle - Examples - Coherent States
... A coherent state is a right eigenstate of the annihilation operator, , which may be represented in terms of Fock states as In the picture where the coherent state is a ... Moreover every squeezed coherent state also saturates the Kennard bound although the individual contributions of position and momentum need not be balanced in ...
Coherent States - Generalizations
... According to Gilmore and Perelomov, who showed it independently, the construction of coherent states may be seen as a problem in group theory, and thus coherent states ... Moreover, these coherent states may be generalized to quantum groups ... to original work, are discussed in detail in Coherent states in mathematical physics ...
Optical Phase Space - Quadratures - Important Result
... Another very important property of the coherent states becomes very apparent in this formalism ... A coherent state is not a point in the optical phase space but rather a distribution on it ... These are only the expected values of and for the state ...

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