Coherent state

In <a href="/facts/Physics/a7aH2y08">physics</a>, specifically in <a href="/facts/Quantum_mechanics/BRc3Mzgr">quantum mechanics</a>, a coherent state is the specific <a href="/facts/Quantum_state/7jbxd7Dx">quantum state</a> of the <a href="/facts/Quantum_harmonic_oscillator/JYA5J0h5">quantum harmonic oscillator</a>, often described as a state that has <a href="/facts/Dynamical_system/782gREl5">dynamics</a> most closely resembling the oscillatory behavior of a <a href="/facts/Harmonic_oscillator/7IQNToGt">classical harmonic oscillator</a>. It was the first example of <a href="/facts/Quantum_dynamics/dmCGsg6B">quantum dynamics</a> when <a href="/facts/Erwin_Schr%C3%B6dinger/wCprepF2">Erwin Schrödinger</a> derived it in 1926, while searching for solutions of the <a href="/facts/Schr%C3%B6dinger_equation/3csgSIWF">Schrödinger equation</a> that satisfy the <a href="/facts/Correspondence_principle/F4RFL8sR">correspondence principle</a>. The quantum harmonic oscillator (and hence the coherent states) arise in the quantum theory of a wide range of physical systems. For instance, a coherent state describes the oscillating motion of a particle confined in a quadratic <a href="/facts/Potential_well/EMQxyqDT">potential well</a> (for an early reference, see e.g. <a href="/facts/Leonard_I._Schiff/gz9hHnJe">Schiff's</a> textbook). 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 <a href="/facts/Eigenvector/8TjEoT8u">eigenvectors</a> of the <a href="/facts/Ladder_operator/kyGdlRjQ">lowering operator</a> and forming an <a href="/facts/Overcompleteness/th2TMz0o">overcomplete</a> family, were introduced in the early papers of <a href="/facts/John_R._Klauder/qySmVjkg">John R. Klauder</a>, e.g. 
In the quantum theory of light (<a href="/facts/Quantum_electrodynamics/zPteAr6G">quantum electrodynamics</a>) and other <a href="/facts/Boson/XtPFcjb5">bosonic</a> <a href="/facts/Quantum_field_theory/VoewsNJV">quantum field theories</a>, coherent states were introduced by the work of <a href="/facts/Roy_J._Glauber/SdAAFreN">Roy J. Glauber</a> 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 <a href="/facts/Mathematical_physics/sLKg8T1G">mathematical physics</a> and in <a href="/facts/Applied_mathematics/qyqklXXm">applied mathematics</a>, with applications ranging from <a href="/facts/Quantization_(physics)/fvs2Jwpn">quantization</a> to <a href="/facts/Signal_processing/Npaja6zb">signal processing</a> and <a href="/facts/Image_processing/zenalNCf">image processing</a> (see <a href="/facts/Coherent_states_in_mathematical_physics/F4KcoumG">Coherent states in mathematical physics</a>). For this reason, the coherent states associated to the <a href="/facts/Quantum_harmonic_oscillator/JYA5J0h5">quantum harmonic oscillator</a> are sometimes referred to as canonical coherent states (CCS), standard coherent states, Gaussian states, or oscillator states.

Coherent state open-in-new

Coherent state