Coherent state problem in quantum mechanics

Thread starter BREAD
Start date Mar 29, 2017
Tags

Coherent Coherent state In quantum mechanics Mechanics Quantum Quantum mechanics State

In summary, a coherent state in quantum mechanics is a state that combines classical and quantum behavior and is described by a wave function with minimum uncertainty. Coherent states have many applications in modeling physical systems, particularly in quantum optics, and are useful for understanding quantum dynamics. They are unique in their properties and present theoretical challenges in terms of consistency and behavior over time. Current research is focused on developing new frameworks and experimental techniques to address the coherent state problem and finding connections to other areas of physics.

Mar 29, 2017

BREAD

Homework Statement

Homework Equations

The Attempt at a Solution

These are what i solved except (e), I have no idea how to solve (e).

Physics news on Phys.org

Mar 29, 2017

PeroK

Science Advisor

Homework Helper

Insights Author

Gold Member

2023 Award

Given you have done parts a) to d), part e) shouldn't be any harder.

What's the definition of an eigenstate?

1. What is a coherent state in quantum mechanics?

A coherent state in quantum mechanics is a state of a quantum system that exhibits characteristics of both classical and quantum behavior. It is a special type of quantum state that is described by a wave function that has a minimum uncertainty in both position and momentum. Coherent states are often used to describe the behavior of quantum systems that are in a state of stable equilibrium.

2. What is the significance of coherent states in quantum mechanics?

Coherent states have many important applications in quantum mechanics. They are used to model the behavior of simple harmonic oscillators, which are fundamental to many physical systems. Coherent states also have applications in quantum optics, where they are used to describe the behavior of light in lasers and other devices. In addition, coherent states are useful for understanding the dynamics of quantum systems and for calculating their properties.

3. How are coherent states different from other quantum states?

Coherent states are unique in that they exhibit both classical and quantum properties. Unlike other quantum states, coherent states have a minimum uncertainty in both position and momentum, which makes them behave more like classical particles. Additionally, coherent states are eigenstates of the annihilation operator, which means they are stable and do not change over time.

4. What is the coherent state problem in quantum mechanics?

The coherent state problem in quantum mechanics refers to the challenge of finding a consistent way to describe the behavior of coherent states. While coherent states have many useful applications, they also present theoretical difficulties, particularly in terms of how they relate to other quantum states and how they behave over time. This problem is still an area of active research in quantum mechanics.

5. How is the coherent state problem being addressed in current research?

Researchers are currently exploring various approaches to address the coherent state problem in quantum mechanics. Some efforts involve developing new mathematical frameworks to better describe the behavior of coherent states. Others involve using advanced experimental techniques to better understand the properties of coherent states in different physical systems. Additionally, there are ongoing efforts to find connections between coherent states and other areas of physics, such as quantum field theory and quantum information theory.