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## Homework Statement

I need to find <x>, <x

^{2}>, <p>, and <p

^{2}> for a particle in the first state of a harmonic oscillator.

## Homework Equations

The harmonic oscillator in the first state is described by [tex]\psi[/tex](x)=A[tex]\alpha[/tex]

^{1/2}*x*e

^{-[tex]\alpha[/tex]*x2/2}. I'm using the definition <Q>=([tex]\int[/tex][tex]\psi[/tex]1*Q*[tex]\psi[/tex])dx where [tex]\psi[/tex]1 is the complex conjugate of [tex]\psi[/tex], and Q is the specific operator.

## The Attempt at a Solution

I solved for <x>, and found it was zero. <p> I'll solve for in a similar fashion. However, for <x

^{2}> and <p

^{2}>, I am unsure of what operators I use. For the <x> operator, it is simply x, so for <x

^{2}>, would I use x

^{2}as an operator?

(note that I the only superscripts here are the ones above e, I don't know why latex is putting all of my symbols so high