I need to find <x>, <x2>, <p>, and <p2> for a particle in the first state of a harmonic oscillator.
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 <x2> and <p2>, I am unsure of what operators I use. For the <x> operator, it is simply x, so for <x2>, would I use x2 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