 Coherent state

$|\alpha ⟩=D(\alpha )|0⟩$ is normalized, satisfies $A|\alpha ⟩=\alpha |\alpha ⟩$, and evolves to a phase times $|\alpha e^{-i\omega t}⟩$.

A coherent state is a specific type of quantum state of a harmonic oscillator that exhibits properties reminiscent of classical oscillators. In quantum mechanics, a coherent state is often associated with the eigenstates of the annihilation operator in the context of quantum optics and quantum mechanics of harmonic oscillators. Key characteristics of coherent states include: 1. **Minimum Uncertainty**: Coherent states minimize the uncertainty relation between position and momentum; they achieve the Heisenberg uncertainty principle's lower bound.