What is a coherent state quantum mechanics?

In physics, specifically in quantum mechanics, a coherent state is the specific quantum state of the quantum harmonic oscillator, often described as a state which has dynamics most closely resembling the oscillatory behavior of a classical harmonic oscillator.

Is group theory used in physics?

In mathematics and abstract algebra, group theory studies the algebraic structures known as groups. Thus group theory and the closely related representation theory have many important applications in physics, chemistry, and materials science. Group theory is also central to public key cryptography.

What is spin coherent state?

Spin states of maximal projection along some direction in space are called (spin) coherent, and are, in many aspects, the “most classical” available. For any spin s, the spin coherent states form a 2-sphere in the projective Hilbert space \mathbb{P} of the system.

Why is a coherent state important?

In quantum mechanics, measuring the vaccum state gives the least fluctuations(in position and momentum) which is the theoretical minimum.. Coherent states are actually displaced vaccum states with the same amount of fluctuations and thus are a valuable tool for experiments.

What is a coherent field?

A light field is called coherent when there is a fixed phase relationship between the electric field values at different locations or at different times. Partial coherence means that there is some (although not perfect) correlation between phase values.

Why is group theory useful?

Group theory addresses the problem of the algebraic equation ax=b. It ensures you that, if you are dealing with a group structure, the equation will for sure have a solution, and that it will be unique! So it is a very important structure.

Are coherent states pure?

It is shown that all pure states whose P representations are nonnegative definite and no more singular than a delta function are coherent states.

Are coherent states classical?

These remarkable quasi-classical states are called coherent states, and were discovered by Schrodinger himself. They are important in many quasi-classical contexts, including laser radiation.

Why are coherent states important?

Coherent state can become a useful and important subject in physics because of its three unique properties: the coherence, the overcompleteness and the intrinsic geometrization. These unique properties, in certain contents, are fundamental to field theory.

What does coherent mean in physics?

coherence
coherence, a fixed relationship between the phase of waves in a beam of radiation of a single frequency. Two beams of light are coherent when the phase difference between their waves is constant; they are noncoherent if there is a random or changing phase relationship.

What are Lie groups used for?

Here is a brief answer: Lie groups provide a way to express the concept of a continuous family of symmetries for geometric objects. Most, if not all, of differential geometry centers around this. By differentiating the Lie group action, you get a Lie algebra action, which is a linearization of the group action.