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.