Quantum Mechanics, Glauber Coherent States of QHO, and superpositions of states

[paris1244bc]

Homework Statement

I need to investigate Glauber Coherent States and I have no clue where to begin.

I need to define a superposition of two coherent states with amplitudes 2.6 and -2.6 in a potential with V0=0.65

Homework Equations

Schrodinger Eqn.
E ψ(x) = -1/2 d^2/dx^2 ψ(x) + V0 x^2/2 ψ(x)

The Attempt at a Solution

No attempt so far =(

This is a coursework question so I'd be grateful if someone will point me in the right direction rater than give me the answer =)

Thanks

 

[mark726]

for posting this question! Investigating Glauber coherent states can be a challenging but rewarding task. Here are some steps you can take to begin your investigation:

1. Start by researching what Glauber coherent states are and what their properties are. This will give you a better understanding of what you will be working with.

2. Familiarize yourself with the Schrodinger equation and how it relates to the coherent states. This will help you understand the mathematical background and how to approach the problem.

3. To define a superposition of two coherent states with amplitudes 2.6 and -2.6, you will need to use the concept of wavefunctions. The superposition of two wavefunctions will give you a new wavefunction which represents the two coherent states together. You can use the general form of a coherent state wavefunction and plug in the given amplitudes to create your superposition.

4. Once you have defined your superposition wavefunction, you can use the Schrodinger equation to solve for the energy of this system. This will give you a better understanding of how the potential V0 affects the system.

5. Finally, you can use your knowledge of Glauber coherent states to analyze the properties of your system and draw conclusions about its behavior.

Remember, it's always helpful to break down a complex problem into smaller, more manageable steps. Good luck with your investigation!