nolanp2 said:i've just encountered coherent states while studying the quantum oscillator, and I'm trying to understand some of the semiclassical properties of them. can someone give me a brief description of what they represent in the system
In simple cases, it often happens that coherent states evolve intoand of how they vary in time?
They are not identical. The set of coherent states forms an (overcomplete) basis for thenolanp2 said:so a coherent state under the hamiltonian of a harmonic
oscillator will be a coherent state for all t? are all coherent states identical?
A coherent state in a quantum oscillator is a quantum state that exhibits classical-like properties. It is described by a wave function that is a Gaussian distribution with a well-defined phase and amplitude. These states are also known as minimum uncertainty states, as they have the lowest possible uncertainty in position and momentum.
Coherent states can be created in a quantum oscillator by applying a coherent state operator to the vacuum state of the oscillator. This operator is a displacement operator that shifts the position and momentum of the vacuum state by a certain amount, creating a coherent state with a well-defined amplitude and phase.
Coherent states in a quantum oscillator have several important properties. They are eigenstates of the annihilation operator, meaning they are stable over time. They also exhibit classical-like behavior, such as following a predictable trajectory in phase space. Additionally, they have the lowest possible uncertainty in position and momentum.
Coherent states differ from other quantum states in that they are eigenstates of the annihilation operator and exhibit classical-like behavior. They also have the lowest possible uncertainty in position and momentum, making them more stable and predictable compared to other quantum states.
Exploring coherent states in a quantum oscillator has many applications in quantum mechanics, such as in quantum computing and quantum communication. Coherent states are also used in quantum metrology, where they can improve the precision of measurements. Additionally, coherent states play a crucial role in understanding the dynamics and behavior of quantum systems.