Coherent State: What Does Re Mean?

In summary, the conversation focused on the coherent state of a harmonic oscillator and an equation involving |psi(x,t)|^2. The term "Re" was mentioned, which typically stands for "real part" and is used when taking the magnitude squared of a sum of complex terms. This concept also applies to classical mechanics, where imaginary solutions are not typically seen.
  • #1
physgirl
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0
Coherent state... "Re"?

So we're talking about coherent state of harmonic oscillator... and for |psi(x,t)|^2, we came up with an equation... that has a term with "Re" in it. Does anyone know what I'm talking about or should I type up the whole equation? What does the "Re" mean?>?>
 
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  • #2
The whole equation would be helpful but usually Re means "real part". Since you're taking the magnitude squared, you have psi times complex conjugate of psi and if psi is a sum of terms it can happen that you get the sum of two cross terms that are complex conjugates of each other.
 
  • #3
Re[blah blah] usually means "take the real part" and Im[blah blah] means "take the imaginary part".

This tends to come up in classical mechanics a bit, too, since you don't really see imaginary solutions to equations of motion.
 

1. What is a coherent state?

A coherent state is a type of quantum state in which the position and momentum of a particle are well-defined and have a constant phase relationship. It is often called the classical limit of the quantum state as it behaves similarly to a classical oscillator.

2. What does "Re" mean in coherent state?

"Re" stands for "real," and it signifies that the coherent state is a real-valued solution to the Schrödinger equation. In other words, the position and momentum of the particle can take on any real value rather than being restricted to discrete energy levels.

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

Coherent states have many important applications in quantum mechanics. They are often used to describe the behavior of a quantum system in the classical limit and are also used in quantum optics to describe the behavior of light. They also have applications in quantum information and computing.

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

Coherent states are unique in that they have a constant phase relationship between position and momentum. Other quantum states, such as energy eigenstates, do not have this property. Coherent states also have a Gaussian probability distribution for position and momentum, making them more similar to classical states.

5. Can coherent states exist in systems other than simple harmonic oscillators?

Yes, coherent states can exist in other systems besides simple harmonic oscillators. They can also be applied to systems with non-linear potentials, such as the anharmonic oscillator. Additionally, they have been studied in systems with multiple degrees of freedom, such as quantum field theory.

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