# Expectation values for a harmonic oscillator

## Homework Statement

I need to find <x>, <x2>, <p>, and <p2> for a particle in the first state of a harmonic oscillator.

## Homework Equations

The harmonic oscillator in the first state is described by $$\psi$$(x)=A$$\alpha$$1/2*x*e-$$\alpha$$*x2/2. I'm using the definition <Q>=($$\int$$$$\psi$$1*Q*$$\psi$$)dx where $$\psi$$1 is the complex conjugate of $$\psi$$, 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

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kuruman
Homework Helper
Gold Member
For the <x> operator, it is simply x, so for <x2>, would I use x2 as an operator?
Yes, that's what you should use.

dx
Homework Helper
Gold Member
(Put the whole equation in the tex barackets instead of individual symbols)

The operator for <x²> is simply multiplication by x², so <x²> = ∫ψ*(x)x²ψ(x)dx, and <p²> is

$$-\int \psi^{*}(x) \hbar^2\frac{\partial^2}{\partial x^2}\psi(x) dx$$

ok, thank you so much guys. It's a good thing I have physics forum to at least make my new ventures into the realm of quantum mechanics a bit easier :)