# Expectation value of operators and squeezing in the even cat state

#### eigenpsi

Problem Statement
I need to derive the equations 7.126 and 7.127(image posted) from Gerry/Knight's quantum optics book. The equations are the expectation values of the square of the quadrature operators for the even cat state.
Relevant Equations
<X1^2>=0.25 + ( (alpha)^2 )/(1+exp(-2alpha^2))

<X2^2>=0.25 - (exp(-2alpha^2)*(alpha)^2)/(1+exp(-2alpha^2))
I started and successfully showed that the expectation of X_1 and X_2 are zero. However the expectation value of X1^2 and X2^2 which I am getting is <X1^2> = 0.25 + \alpha^2 and <X2^2> = 0.25.

How do I derive the given equations?

#### Attachments

• 10.5 KB Views: 26
Last edited:
Related Advanced Physics Homework News on Phys.org

"Expectation value of operators and squeezing in the even cat state"

### Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving